Subtract the polynomials. See Example 5. a56q9 45q8b a14q938q8b

Expressions such as x4, 103, and (5t)2 are called ______ expressions.

Match each expression below with the proper description on the next page. a5 a3 (a8 ) 4 a a6 a b 3 (a4 b2 ) 5 a8 a2 a. Product of exponential expressions with the same base b. Quotient of exponential expressions with the same base c. Power of an exponential expression d. Power of a product e. Power of a quotient

Fill in the blanks. a. (3x)4 b. (5y)(5y)(5y)

Fill in the blanks. a. x x b. xmxn c. (xy) n d. (ab ) c e. xm xn f. a a b b n

To simplify each expression, determine whether you add, subtract, multiply, or divide the exponents. a. x8 x2 b. b6 b9 x c. (n8 ) 4 d. (a4 b2 ) 5

a. To simplify (2y3 z 2 ) 4, what factors within the parentheses must be raised to the fourth power? b. To simplify 1 y3 z2 24 , what two expressions must be raised to the fourth power?

Simplify each expression, if possible. a. x2 x2 b. x2 x2 x c. x x 2 x x d. x2 x x 2

Simplify each expression, if possible. a. x3  x2 b. x3 x2 c. 42 24 d. x3 y 2

Complete each solution to simplify each expression. (x x 4 x2 ) 3 (

Complete each solution to simplify each expression. a3 a4 a2 a2 a )

Fill in the blanks. a. We read as nine to the fourth _____ . b. We read (a2 b6 )(a4 b5 as the _____ of a2 b6 times the of . c. We read as 3 to the _____ power, raised to the _____ power.

Fill in the blanks. a. We read as n _____ times n ____ times n. b. We read as x to the seventh power ____ by x to the ______ power. c. We read as the of b 5, to the sixth power, times the _____ of b 5, raised to the ______ power.

Identify the base and the exponent in each expression. See Example 1. a. 43 b. 43 c. (4)3

Identify the base and the exponent in each expression. See Example 1. a. x5 b. x5 c. (x)5

Identify the base and the exponent in each expression. See Example 1. a. (3x)2 b. 3x2 c. (3x)2 

Identify the base and the exponent in each expression. See Example 1. a. 1 3 x6 b. a 1 3 xb 6 c. a 1 3 xb 6

Identify the base and the exponent in each expression. See Example 1. a. 9m12 b. 9m)12 c. 9m12

Identify the base and the exponent in each expression. See Example 1. a. (y 9)4 b. y 94 (y c. 8(y 9)4 y

Write each expression in an equivalent form using an exponent. See Example 2. 4t 4t 4t 4t

Write each expression in an equivalent form using an exponent. See Example 2. 5u(5u)(5u)(5u)(5u)

Write each expression in an equivalent form using an exponent. See Example 2. 4 t t t t t 

Write each expression in an equivalent form using an exponent. See Example 2. 5 u u u

Write each expression in an equivalent form using an exponent. See Example 2. t 2 t 2 t 2 

Write each expression in an equivalent form using an exponent. See Example 2. x c x c x c x c t

Write each expression in an equivalent form using an exponent. See Example 2. (x  y)(x  y)

Write each expression in an equivalent form using an exponent. See Example 2. (m 4)(m 4)

Use the product rule for exponents to simplify each expression. Write the results using exponents. See Example 3. 53 54

Use the product rule for exponents to simplify each expression. Write the results using exponents. See Example 3. 34 36 5

Use the product rule for exponents to simplify each expression. Write the results using exponents. See Example 3. bb2 b3

Use the product rule for exponents to simplify each expression. Write the results using exponents. See Example 3. aa3 a5 b

Use the product rule for exponents to simplify each expression. Write the results using exponents. See Example 3. y  2)5 (y  2)2

Use the product rule for exponents to simplify each expression. Write the results using exponents. See Example 3. (t 1)5 (t 1)3 (y

Use the product rule for exponents to simplify each expression. Write the results using exponents. See Example 3. (a ) 2 b3 )(a3 b3 )

Use the product rule for exponents to simplify each expression. Write the results using exponents. See Example 3. (u3 v 5 )(u4 v 5

Find an expression that represents the area or volume of each figure. Recall that the formula for the volume of a rectangular solid is length width height. See Example 4. a5 mi a5 mi

Find an expression that represents the area or volume of each figure. Recall that the formula for the volume of a rectangular solid is length width height. See Example 4. y9 yd y2 yd

Find an expression that represents the area or volume of each figure. Recall that the formula for the volume of a rectangular solid is length width height. See Example 4. x4 ft x2 ft x3 ft

Find an expression that represents the area or volume of each figure. Recall that the formula for the volume of a rectangular solid is length width height. See Example 4. x7 cm x7 cm x7 cm

Use the quotient rule for exponents to simplify each expression. Write the results using exponents. See Example 5. 812 84

Use the quotient rule for exponents to simplify each expression. Write the results using exponents. See Example 5. 104 102

Use the quotient rule for exponents to simplify each expression. Write the results using exponents. See Example 5. x15 x3

Use the quotient rule for exponents to simplify each expression. Write the results using exponents. See Example 5. y 6 y3

Use the quotient rule for exponents to simplify each expression. Write the results using exponents. See Example 5. (3.7p) 7 (3.7p) 2

Use the quotient rule for exponents to simplify each expression. Write the results using exponents. See Example 5. (0.25y) 9 (0.25y) 3

Use the quotient rule for exponents to simplify each expression. Write the results using exponents. See Example 5. c 3 d7 cd

Use the quotient rule for exponents to simplify each expression. Write the results using exponents. See Example 5. r 8 s 9 rs

Use the product and quotient rules for exponents to simplify each expression. See Example 6. y 3 y 4 yy2

Use the product and quotient rules for exponents to simplify each expression. See Example 6. b4 b5 b2 b3

Use the product and quotient rules for exponents to simplify each expression. See Example 6. a2 a3 a4 a8

Use the product and quotient rules for exponents to simplify each expression. See Example 6. h3 h6 h h9

Use the power rule for exponents to simplify each expression. Write the results using exponents. See Example 7. (32 ) 4

Use the power rule for exponents to simplify each expression. Write the results using exponents. See Example 7. (43 ) 3

Use the power rule for exponents to simplify each expression. Write the results using exponents. See Example 7. [(4.3)3 ] 8

Use the power rule for exponents to simplify each expression. Write the results using exponents. See Example 7. [(1.7)9 ] 8

Use the power rule for exponents to simplify each expression. Write the results using exponents. See Example 7. (m50) 10

Use the power rule for exponents to simplify each expression. Write the results using exponents. See Example 7. (n25) 4

Use the power rule for exponents to simplify each expression. Write the results using exponents. See Example 7. (y 5 ) 3

Use the power rule for exponents to simplify each expression. Write the results using exponents. See Example 7. (b3 ) 6

Use the product and power rules for exponents to simplify each expression. See Example 8. (x2 x3 ) 5

Use the product and power rules for exponents to simplify each expression. See Example 8. (y 3 y 4 ) 4

Use the product and power rules for exponents to simplify each expression. See Example 8. (p2 p3 ) 5

Use the product and power rules for exponents to simplify each expression. See Example 8. (r 3 r 4 ) 2

Use the product and power rules for exponents to simplify each expression. See Example 8. (t 3 ) 4 (t 2 ) 3

Use the product and power rules for exponents to simplify each expression. See Example 8. (b2 ) 5 (b3 ) 2

Use the product and power rules for exponents to simplify each expression. See Example 8. (u4 ) 2 (u3 ) 2

Use the product and power rules for exponents to simplify each expression. See Example 8. (v 5 ) 2 (v 3 ) 4

Use the power of a product rule for exponents to simplify each expression. See Example 9. 6a) 2

Use the power of a product rule for exponents to simplify each expression. See Example 9. (3b) 3

Use the power of a product rule for exponents to simplify each expression. See Example 9. (5y) 4

Use the power of a product rule for exponents to simplify each expression. See Example 9. (4t) 4

Use the power of a product rule for exponents to simplify each expression. See Example 9. (2r 2 s 3 ) 3

Use the power of a product rule for exponents to simplify each expression. See Example 9. (2x2 y 4 ) 5

Use the power of a product rule for exponents to simplify each expression. See Example 9. a1 3 y 2 z 4 b 5

Use the power of a product rule for exponents to simplify each expression. See Example 9. a1 4 t 3 u8 b 2

Use rules for exponents to simplify each expression. See Example 10. (ab2 ) 3 a2 b

Use rules for exponents to simplify each expression. See Example 10. (m3 n4 ) 3 m3 n6

Use rules for exponents to simplify each expression. See Example 10. (r 4 s 3 ) 4 r 3 s 9

Use rules for exponents to simplify each expression. See Example 10. (x2 y 5 ) 5 x6 y 2

Use rules for exponents to simplify each expression. See Example 11. (6k) 7 (6k)

Use rules for exponents to simplify each expression. See Example 11. (3a) 12 (3a) 10

Use rules for exponents to simplify each expression. See Example 11. (3q) 5 (3q) 3

Use rules for exponents to simplify each expression. See Example 11. ab) 8 (ab) 4

Use the power of a quotient rule for exponents to simplify each expression. See Example 12. a a b b 3

Use the power of a quotient rule for exponents to simplify each expression. See Example 12. a r s b 4

Use the power of a quotient rule for exponents to simplify each expression. See Example 12. a 8a2 11b5 b 2

Use the power of a quotient rule for exponents to simplify each expression. See Example 12. a 7g4 6h3 b 2

Simplify each expression, if possible. a x2 y 3 b 5

Simplify each expression, if possible. a u4 v 2 b 6

Simplify each expression, if possible. y 3 y 2 y 4

Simplify each expression, if possible. y 4 yy6

Simplify each expression, if possible. 159 156

Simplify each expression, if possible. 2513 257

Simplify each expression, if possible. t 5 t 6 t t 2 t 3

Simplify each expression, if possible. m5 m12m m7 m4

Simplify each expression, if possible. (k  2)15 (k  2)

Simplify each expression, if possible. (m 8)20 (m 8) (

Simplify each expression, if possible. cd4 cd

Simplify each expression, if possible. ab3 ab4 c

Simplify each expression, if possible. a y 3 y 5 yy2 b 3

Simplify each expression, if possible. a s 5 s 6 s 2 s 2 b 4

Simplify each expression, if possible. s 2 s 2 s 2 s 3 s

Simplify each expression, if possible. w4 w4 w4 w2 w

Simplify each expression, if possible. (6a3 b2 ) 3

Simplify each expression, if possible. (10r 3 s 2 ) 2

Simplify each expression, if possible. a 3m4 2n5 b 5

Simplify each expression, if possible. a 2s 2 3t 5 b 5

Simplify each expression, if possible. (a2 b2 ) 15 (ab) 9

Simplify each expression, if possible. (s 3 t 3 ) 4 (st) 2

Simplify each expression, if possible. (n4 n) 3 (n3 ) 6

Simplify each expression, if possible. (y 3 y) 2 (y 2 ) 2

Simplify each expression, if possible. (6h) 8 (6h) 6

Simplify each expression, if possible. (7r) 10 (7r) 8

Simplify each expression, if possible. x4 y 7 xy3

Simplify each expression, if possible. p7 q10 p2 q7

Simplify each expression, if possible. a m 3 b 4

Simplify each expression, if possible. a n 5 b 3

Simplify each expression, if possible. a. a3 a3 b. (a3 ) 3 c. a3 a3 (

Simplify each expression, if possible. a. (m5 ) 7 b. m5 m7 ( c. m5  m7

Simplify each expression, if possible. a. b3 b2 b4 b. (b3 b2 ) 4 c. b3 b2 b4

Simplify each expression, if possible. a. (2n n 4 n) 5 b. 2n4 (2n n c. a 2n4 n b 5

Art History. Leonardo da Vincis drawing relating a human figure to a square and a circle is shown. Find an expression for the following: a. The area of the square if the mans height is 5x feet b. The area of the circle if the waist-to-feet distance is 3a feet. Leave in your answer.

Packaging. A bowling ball fits tightly against all sides of a cardboard box that it is packaged in. Find expressions for the volume of the ball and box. Leave p in your answer. 6x in. 6x in. 6x in.

Childbirth. Mr. and Mrs. Emory Harrison, of Johnson City, Tennessee, had 13 sons in a row during the 1940s and 1950s. The probability of a family of 13 children all being male is 1 1 2 2 13. Evaluate this expression.

Toys. A Super Ball is dropped from a height of 1 foot and always rebounds to four-fifths of its previous height. The rebound height of the ball after the third bounce is 1 4 5 2 3 feet. Evaluate this expression. Is the third bounce more or less than 1 2 foot high?

Explain the mistake in the following work. a. 23 22 45 1,024 b. (5d2 3 15d6 2

Explain why we can simplify x4 x5, but cannot simplify x . 4 x5

Match each equation with its graph below. y 2x  1 y 11 1 1 2 3 2 23 2 3 y x 11 1 1 3 2 3 23 2 3 y x 11 1 1 2 3 2 3 23 2 y x 11 1 1 2 3 2 3 23 2 3 y

Match each equation with its graph below. y 3x  1 11 1 1 2 3 2 23 2 3 y x 11 1 1 3 2 3 23 2 3 y x 11 1 1 2 3 2 3 23 2 y x 11 1 1 2 3 2 3 23 2 3 y

Match each equation with its graph below. y 3 11 1 1 2 3 2 23 2 3 y x 11 1 1 3 2 3 23 2 3 y x 11 1 1 2 3 2 3 23 2 y x 11 1 1 2 3 2 3 23 2 3 y

Match each equation with its graph below. x 3 11 1 1 2 3 2 23 2 3 y x 11 1 1 3 2 3 23 2 3 y x 11 1 1 2 3 2 3 23 2 y x 11 1 1 2 3 2 3 23 2 3 y

Simplify each expression. The variables represent natural numbers. a. x2mx3m b. (y5c ) 4 c. m 4 8x m4x d . (2a6y ) m 4

Evaluate the following expression without using a calculator: (108,642)4 (54,321)4

In the expression 51, the exponent is ______ a integer.

xn is the ______ of xn.

We read a0cas a to the _____ power.

We read 34 as 3 to the power _____ _____ .

Complete the table. Expression Base Exponent 10a0 (2)3 71 1 3 y 2 8 6x5 42

Complete each rule for exponents. a. x m xn b. x0 x m c. (x m)nx d. (xy)n (x m e. a x y b n( f. xn a x g. 1 xn h. xm y n 1 i. xm xn x j. a x y b n

Complete each table. 2 1 0 2 1 3x x

Complete each table. 2 1 0 2 1 (9) x x

Fill in the blanks. a. b. c. A factor can be moved from the denominator to the numerator or from the numerator to the denominator of a fraction if the ______ of its exponent is changed. 1 t 2 6 t 3 1 2 6 5 52 63 d. A fraction raised to a power is equal to the _____ of the fraction raised to the opposite power. a 3 d b 2 a d 3 b

Determine whether each statement is true or false. a. 62 36 b. 62 1 36 c. x3 y 2 y 2 x3 d. 6x5 y 6 y 6 6x5

Complete each solution to simplify each expression. y5 y3 ) 5 1 2 5 y 1 y 6

Complete each solution to simplify each expression. a a2 b a3 b3 b 3 1a2 b1 2 3 a15 b a b (a

Simplify each expression. See Example 1. 70

Simplify each expression. See Example 1. 90

Simplify each expression. See Example 1. a 1 4 b 0

Simplify each expression. See Example 1. a 3 8 b 0

Simplify each expression. See Example 1. 2x0

Simplify each expression. See Example 1. 8t 0

Simplify each expression. See Example 1. 5 2x0

Simplify each expression. See Example 1. 4 3a0

Express using positive exponents and simplify, if possible. See Example 2. 22

Express using positive exponents and simplify, if possible. See Example 2. 72

Express using positive exponents and simplify, if possible. See Example 2. 61

Express using positive exponents and simplify, if possible. See Example 2. 51 6

Express using positive exponents and simplify, if possible. See Example 2. b5

Express using positive exponents and simplify, if possible. See Example 2. c4

Express using positive exponents and simplify, if possible. See Example 2. (5)1

Express using positive exponents and simplify, if possible. See Example 2. (8)1 (

Express using positive exponents and simplify, if possible. See Example 2. 22 41

Express using positive exponents and simplify, if possible. See Example 2. 91 92 2

Express using positive exponents and simplify, if possible. See Example 2. 90  91

Express using positive exponents and simplify, if possible. See Example 2. 71  70

Simplify. Do not use negative exponents in the answer. See Example 3. 15g6

Simplify. Do not use negative exponents in the answer. See Example 3. 16t 3

Simplify. Do not use negative exponents in the answer. See Example 3. 5x3

Simplify. Do not use negative exponents in the answer. See Example 3. 27m3

Simplify. Do not use negative exponents in the answer. See Example 3. 33

Simplify. Do not use negative exponents in the answer. See Example 3. 63

Simplify. Do not use negative exponents in the answer. See Example 3. 82

Simplify. Do not use negative exponents in the answer. See Example 3. 42

Simplify. Do not use negative exponents in the answer. See Example 4. 1 53

Simplify. Do not use negative exponents in the answer. See Example 4. 1 33

Simplify. Do not use negative exponents in the answer. See Example 4. 8 s 1

Simplify. Do not use negative exponents in the answer. See Example 4. 6 k2

Simplify. Do not use negative exponents in the answer. See Example 4. 24 31

Simplify. Do not use negative exponents in the answer. See Example 4. 72 23

Simplify. Do not use negative exponents in the answer. See Example 4. 4d 1 p10

Simplify. Do not use negative exponents in the answer. See Example 4. 9m1 n30

Simplify. See Example 5. a 1 6 b 2

Simplify. See Example 5. a 1 7 b 2

Simplify. See Example 5. a 1 2 b 3

Simplify. See Example 5. a 1 5 b 3

Simplify. See Example 5. a c d b 8

Simplify. See Example 5. a a x b 10

Simplify. See Example 5. a 3 mb 4

Simplify. See Example 5. a 2 t b 4

Simplify. Do not use negative exponents in the answer. See Example 6. y 8 y 2

Simplify. Do not use negative exponents in the answer. See Example 6. m10 m6 y

Simplify. Do not use negative exponents in the answer. See Example 6. b7 b14

Simplify. Do not use negative exponents in the answer. See Example 6. c 9 c 14

Simplify. Do not use negative exponents in the answer. See Example 6. y 4 y 5

Simplify. Do not use negative exponents in the answer. See Example 6. t 7 t 10

Simplify. Do not use negative exponents in the answer. See Example 6. h5 h2

Simplify. Do not use negative exponents in the answer. See Example 6. y3 y 4

Simplify. Do not use negative exponents in the answer. See Example 6. (x4 ) 3

Simplify. Do not use negative exponents in the answer. See Example 6. (y3 ) 2

Simplify. Do not use negative exponents in the answer. See Example 6. (b2 ) 4

Simplify. Do not use negative exponents in the answer. See Example 6. (n3 ) 5

Simplify. Do not use negative exponents in the answer. See Example 6. (6s 4 t 7 ) 2

Simplify. Do not use negative exponents in the answer. See Example 6. (11r 10s 3 ) 2

Simplify. Do not use negative exponents in the answer. See Example 6. a 4 x3 b 3

Simplify. Do not use negative exponents in the answer. See Example 6. a 2 b5 b 2

Simplify. Do not use negative exponents in the answer. See Example 7. y 3 y4 y2

Simplify. Do not use negative exponents in the answer. See Example 7. x12 x3 x4

Simplify. Do not use negative exponents in the answer. See Example 7. a5 a9 a8

Simplify. Do not use negative exponents in the answer. See Example 7. b2 b3 b9

Simplify. Do not use negative exponents in the answer. See Example 7. 21 a4 b2 32 a2 b4

Simplify. Do not use negative exponents in the answer. See Example 7. 62 b9 c 3 53 b4 c8

Simplify. Do not use negative exponents in the answer. See Example 7. a y 3 z 2 y 4 z 3b 2

Simplify. Do not use negative exponents in the answer. See Example 7. a xy3 x1 y 1 b 3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a a4 2b b 3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a n8 9mb 2

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. r 50 r 70

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. m30 m4

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a5 b2

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. r 6 s 1

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. (10)3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. (9)2

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a a2 b3 ab4 b 0

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a xyz x2 y b 0

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 92 s 6 t 43 s 4 t 5

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 25 m10n6 52 m6 n10

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. (2u2 v 5 ) 5

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. (3w8 x3 ) 4

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a y 4 3 b 2

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a p3 2 b 2

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 15x0 y

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 24g0 h2 

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a 4 h10 b 2

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a x4 3 b 4

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. x3 x3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. y 2 y 2 x

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0.a c 3 d 4 c1 d5 b 3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. a s 2 t 8 s 9 t 2 b 4

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 15(6x) 0

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 4(12y) 0

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 22 g2 h3 91 h3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0.51 x2 y 3 82 x11

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 5d 2 ) 3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 9s 6 ) 2

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. x2 y 2 x5 y 3b 4

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. r 4 s 3 r 3 s 7 b 3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. (2x3 y 2 ) 5

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 3u2 v 3 ) 3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. t(t 2 ) 2 t 5

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. d(d 3 ) 3 d 7

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 4s 5 t 2

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. 9k8 m2

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. (x4 x3 ) 3

Simplify. Do not use negative exponents in the answer. Assume that no variables are 0. (y 2 y) 3

Simplify. Do not use negative exponents in the answer. See Example 7. a. 81 b. 81 c. (8)1 d. (8)1

Simplify. Do not use negative exponents in the answer. See Example 7. a. 92 b. 92 c. (9)2 d. (9)2

Simplify. Do not use negative exponents in the answer. See Example 7. a. 4xy2 b. (4xy)2 c. 4x 2 y d.42xy

Simplify. Do not use negative exponents in the answer. See Example 7. a. a r s b 1 b. r 1 s c. r s 1 d. r 1 s 1

Sound Engineering Technician The faintest sound that the typical human ear can detect (called the threshold of hearing) has an intensity of 1012 units. A sound intensity of 104 units will cause an instant rupture of the eardrum. Consider the types of sounds in the table below. In the intensity column, write the most appropriate exponential expression from the following list. Each expression is used only once. (Source: physicsclassroom.com) Lowest intensity Greatest intensity 102 101 104 106 1010 125. Type of sound Intensity Front row rock concert Normal conversation Vacuum cleaner Military jet takeoff Whisper

Electronics. The total resistance of a certain circuit is given by R a 1 R1 1 R2 b 1 R3 R Find R if R1 4, R2 2 R3 and R3 1.

Explain how you would help a friend understand that 23 is not equal to -8 .

Explain each error. a. 5x2 y 2 y2 5x2 b. 42  1 16

Find the slope of the line that passes through the given points. (1, 4) and (3, 7)

Find the slope of the line that passes through the given points. (1, 3) and (3, 1)

Find the slope of the line that passes through the given points. Write an equation of the line having slope 3 4 and y-intercept -5.

Find the slope of the line that passes through the given points. Find an equation of the line that passes through (4, 4) and (6, 6). Write the answer in slopeintercept form.

Simplify each expression. Do not use negative exponents in the answer. The variable represents a positive integer. a. r 5mr 6m b. x3m x6m

Write an expression equivalent to a 2x3 y7 3z 5 b 9 that involves only negative exponents.

4.84 105 is written in ______ notation. 484,000 is written in ______ notation.

103, 1050 and 104 are ______ of 10.

When we multiply a decimal by 105, the decimal point moves 5 places to the _____ . When we multiply a decimal by 107, the decimal point moves 7 places to the _____ .

Describe the procedure for converting a number from scientific notation to standard form. a. If the exponent on the base of 10 is positive, move the decimal point the same number of places to the _____ as the exponent. b. If the exponent on the base of 10 is negative, move the decimal point the same number of places to the ______ as the absolute value of the exponent.

a. When a real number greater than or equal to 10 is written in scientific notation, the exponent on 10 is a _______ integer. b. When a real number between 0 and 1 is written in scientific notation, the exponent on 10 is a _____ integer.

The arrows show the movement of a decimal point. By what power of 10 was each decimal multiplied? a. 0.0 0 0 0 0 0 5 5 6 b. 8, 0 4 1, 0 0 0, 0 0 0 .

Fill in the blanks to write each number in scientific notation. a. 10 3 7,70 b. 500,000 3 105 c. 114,000,000 1.14 10

Fill in the blanks to write each number in scientific notation. a. 0.0082 103 b. 0.0000001 107 c. 0.00003457 3.457 10

Write each expression so that the decimal numbers are grouped together and the powers of ten are grouped together. a. (5.1 109 )(1.5 1022) b. 8.8 1030 2.2 1019

Simplify each expression. a. 1024 1033 b. 1050 1036 c. 1015 1027 1040

Fill in the blanks. A positive number is written in scientific notation when it is written in the form N 10n, where  N and n is an _______.

Express each power of 10 in fraction form and decimal form. a. 103 b. 106

Convert each number to standard notation. See Example 1. 2.3 102

Convert each number to standard notation. See Example 1. 3.75 104

Convert each number to standard notation. See Example 1. 8.12 105

Convert each number to standard notation. See Example 1. 1.2 103

Convert each number to standard notation. See Example 1. 1.15 103

Convert each number to standard notation. See Example 1. 4.9 102

Convert each number to standard notation. See Example 1. 9.76 104

Convert each number to standard notation. See Example 1. 7.63 105

Convert each number to standard notation. See Example 1. 6.001 106

Convert each number to standard notation. See Example 1. 9.998 105

Convert each number to standard notation. See Example 1. 2.718 100

Convert each number to standard notation. See Example 1. 3.14 100

Convert each number to standard notation. See Example 1. 6.789 102

Convert each number to standard notation. See Example 1. 4.321 101

Convert each number to standard notation. See Example 1. 2.0 105

Convert each number to standard notation. See Example 1. 7.0 106

Write each number in scientific notation. See Example 2. 23,000

Write each number in scientific notation. See Example 2. 4,750

Write each number in scientific notation. See Example 2. 1,700,000

Write each number in scientific notation. See Example 2. 290,000

Write each number in scientific notation. See Example 2. 0.062

Write each number in scientific notation. See Example 2. 0.00073

Write each number in scientific notation. See Example 2. 0.0000051

Write each number in scientific notation. See Example 2. 0.04

Write each number in scientific notation. See Example 2. 5,000,000,000

Write each number in scientific notation. See Example 2. 7,000,000

Write each number in scientific notation. See Example 2. 0.0000003

Write each number in scientific notation. See Example 2. 0.0001

Write each number in scientific notation. See Example 2. 909,000,000

Write each number in scientific notation. See Example 2. 7,007,000,000

Write each number in scientific notation. See Example 2. 0.0345

Write each number in scientific notation. See Example 2. 0.000000567

Write each number in scientific notation. See Example 2. 9

Write each number in scientific notation. See Example 2. 2

Write each number in scientific notation. See Example 2. 11

Write each number in scientific notation. See Example 2. 55

Write each number in scientific notation. See Example 2. 1,718,000,000,000,000,000

Write each number in scientific notation. See Example 2. 44,180,000,000,000,000,000

Write each number in scientific notation. See Example 2. 0.0000000000000123

Write each number in scientific notation. See Example 2. 0.0000000000000000555

Write each number in scientific notation. See Example 2. 73 104

Write each number in scientific notation. See Example 2. 99 105

Write each number in scientific notation. See Example 2. 201.8 1015

Write each number in scientific notation. See Example 2. 154.3 1017

Write each number in scientific notation. See Example 2. 0.073 103

Write each number in scientific notation. See Example 2. 0.0017 104

Write each number in scientific notation. See Example 2. 36.02 1020

Write each number in scientific notation. See Example 2. 56.29 1030

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. (3.4 102 )(2.1 103)

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. (4.1 103 )(3.4 104)

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. (8.4 1013)(4.8 109)

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. (5.5 1015)(2.2 1013)

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. 2.24 104 5.6 107

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. 2.47 105 3.8 105

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. 9.3 102 3.1 102

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. 7.2 106 1.2 108

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. 0.00000129 0.0003

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. 169,000,000,000 26,000,000

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. (0.0000000056)(5,500,000)

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. . (0.000000061)(3,500,000,000)

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. 96,000 (12,000)(0.00004)

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. (0.48)(14,400,000) 96,000,000

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. 2,475 (132,000,000,000,000)(0.25)

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation. See Examples 3 and 4. 147,000,000,000,000 (0.000049)(25)

Find each power. (456.4)6

Find each power. (0.009)6

Find each power. 2255

Find each power. a 1 3 b 55

Astronomy. The distance from Earth to Alpha Centauri (the nearest star outside our solar system) is about 25,700,000,000,000 miles. Write this number in scientific notation.

Water. According to the U.S. Geological Survey, the total water supply of the world is 366,000,000,000,000,000,000 gallons. Write this number in scientific notation.

Earth, Sun, Moon. The surface area of Earth is 1.97 108 square miles, the surface area of the sun is 1.09 1017 square miles, and the surface area of the moon is 1.46 107 square miles. Convert each number to standard notation.

Atoms. The number of atoms in 1 gram of iron is approximately 1.08 1022. Convert this number to standard notation.

Sand. The mass of one grain of beach sand is approximately 0.00000000045 ounce. Write this number in scientific notation.

Molecules. The mass of a water molecule is approximately 0.000000000000000000000001056 ounce. Write this number in scientific notation.

Wavelengths. Examples of the most common types of electromagnetic waves are given in the table in the next column. List the wavelengths in order from shortest to longest. This distance between the two crests of the wave is called the wavelength. Wave motion Type Use Wavelength (in meters) visible light lighting infrared photography x-ray medical radio wave communication gamma ray treating cancer microwave cooking ultraviolet sun lamp 6.1 108 1.1 102 8.9 1014 3.0 102 2.3 1011 3.7 105 9.3 106

Exploration. On July 4, 1997, the Pathfinder, carrying the rover vehicle called Sojourner, landed on Mars. The distance from Mars to Earth is approximately 3.5 107 miles. Use scientific notation to express this distance in feet. (Hint: 5,280 feet 1 mile.)

Sound Engineering Technician The speed of sound in air is approximately 3.3 104 centimeters per second. Use scientific notation to express this speed in kilometers per second. (Hint: 100 centimeters 1 meter and 1,000 meters 1 kilometer.)

Protons. The mass of one proton is approximately 1.7 1024 gram. Use scientific notation to express the mass of 1 million protons.

Light Years. One light year is about 5.87 1012 miles. Use scientific notation to express this distance in feet. (Hint: 5,280 feet 1 mile.)

Oil. As of 2009, Saudi Arabia was believed to have crude oil reserves of about 2.65 1011 barrels. A barrel contains 42 gallons of oil. Use scientific notation to express Saudi Arabias oil reserves in gallons. (Source: British Petroleum)

Insured Deposits. As of June 2009, the total insured deposits in U.S. banks and savings and loans was approximately 7.6 1012 dollars. If this money was invested at a rate of 4% simple annual interest, how much would it earn in 1 year? Use scientific notation to express the answer. (Source: Federal Deposit Insurance Corporation.)

Currency. As of December 2009, the number of $20 bills in circulation was approximately 6.4 109. What was the total value of the currency? Express the answer in scientific notation and standard notation. (Source: The Federal Reserve.)

Powers of 10. In the United States, we use Latin prefixes in front of illion to name extremely large numbers. Write each number in scientific notation. One million: 1,000,000 One billion: 1,000,000,000 One trillion: 1,000,000,000,000 One quadrillion: 1,000,000,000,000,000 One quintillion: 1,000,000,000,000,000,000

Supercomputers. As of June 2009, the worlds fastest computer was the Cray Jaguar, owned by the Oak Ridge National Laboratory in Tennessee. If it could make 1.75 1015 calculations in one second, how many could it make in one minute? Answer in scientific notation. (Source: datacenterknowledge.com)

In what situations would scientific notation be more convenient than standard notation?

To multiply a number by a power of 10, we move the decimal point. Which way, and how far? Explain.

2.3 103 contains a negative sign but represents a positive number. Explain.

Explain why 237.8 108 is not written in scientific notation.

If y 1, find the value of 5y 55

What is the -intercept of the graph of y 3x  5?

Counseling. At the end of her first year of practice, a family counselor had 75 clients. At the end of her second year, she had 105 clients. If a linear trend continues, write an equation that gives the number of clients the counselor will have at the end of years.

Is (0, 5) a solution of 2x 3y  14?

Consider 2.5 104. Answer the following questions in scientific notation form. a. What is its opposite? b. What is its reciprocal?

a. Write the numbers one million and one millionth in scientific notation. b. By what number must we multiply one millionth to get one million?

A _____ is a term or a sum of terms in which all variables have whole-number exponents and no variable appears in a denominator.

The ______ of a polynomial are separated by + symbols.

x3 6x2 9x 2 is a polynomial in _____ variable, and is written in _____ powers of x, c 3 2c2d d2 x and is a polynomial in _____variables and is written in _____ powers of d.

For the polynomial 6x2 3x 1d, the _____ term is 6x2 , and the leading _____ is 6. The ____ term is -1.

A _____ is a polynomial with exactly one term. A _____ is a polynomial with exactly two terms. A ____ is a polynomial with exactly three terms.

The _____ of the term 3x7 is 7 because x appears as a factor 7 times: 3  x  x  x  x  x  x  x.

To _____ the polynomial x 2 2x 1 for x  6, we substitute 6 for and follow the rules for the order of operations.

The graph ofy  x2 is a cup-shaped curve called a ______.

Determine whether each expression is a polynomial. a. b. c. d. e. f. a4 a3 a2 x a 2 y 2 x 3 x 1 2 1 2x 3 x 4 x 5x 3 5x 2 2 y  x 2

Fill in the blank so that the term has degree 5. a. 9x b. 2 3 xy

Make a term-coefficient-degree table like that shown in Example 1 for each polynomial. 8x 2 x 7 Term Coefficient Degree Term Degree of the polynomial:

Make a term-coefficient-degree table like that shown in Example 1 for each polynomial. y 4 y 3 16y 2 3y Term Coefficient Degree Degree of the polynomial:

Make a term-coefficient-degree table like that shown in Example 1 for each polynomial. 8a6 b3 27ab Term Coefficient Degree Degree of the polynomial:

Make a term-coefficient-degree table like that shown in Example 1 for each polynomial. 1.2c4 2.4c2 d2 3.6d4 8a6 Term Coefficient Degree Degree of the polynomial:

a. Write x 9 3x2 5x3 in descending powers of x. b. Write 2xy y2 x2 in ascending powers of y.

Complete the solution. Evaluate 2x2 3x 1 for x 2. 2x2 3x 1 22 3 1 2( 3( ) ) 1 ) )  (6) 1  2

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 3x 7 3

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 3y 5

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. y 2 4y 3

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 9xy

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 3 2 z 2

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 3 5 x 4 2 5 x 3 3 5 x 1 3

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. t 32

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 12z 4 t

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 2 23s 31 12

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 2x 3 5x 2 6x 3 2

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 6x 5 x 4 3x 3 7 2x

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. x 3

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 3m3 n 4m2 n2 mn 1 x

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 4p3 q2 7p2 q3 pq4 q5 3m3

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. 2a2 3ab b2 4

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. See Example 1. a3 b ab3 2

Find the degree of each polynomial. See Example 1. 3x4

Find the degree of each polynomial. See Example 1. 3x5

Find the degree of each polynomial. See Example 1. 2x 3x 2 1

Find the degree of each polynomial. See Example 1. 5x 4 3x 2 3x 2 3

Find the degree of each polynomial. See Example 1. 1 2 3 x 5

Find the degree of each polynomial. See Example 1. 1 2 y 3 4y 1 2

Find the degree of each polynomial. See Example 1. 5r 2 s 2 r 3 s 3 1

Find the degree of each polynomial. See Example 1. 4r 2 s 3 5r 2 s 8 5

Find the degree of each polynomial. See Example 1. x b 12 3x 2 y 3 4

Find the degree of each polynomial. See Example 1. 17ab5 12a3 x b 1

Find the degree of each polynomial. See Example 1. 38 2

Find the degree of each polynomial. See Example 1. 24

Find the degree of each polynomial. See Example 1. 3 16 2 m7 3 4 m18 3

Find the degree of each polynomial. See Example 1. 7 8 t 10 1 8 t 3 16 2

Find the degree of each polynomial. See Example 1. 5.5tw 6.5t 2 w 7.5t 3 7

Find the degree of each polynomial. See Example 1. 0.4h 0.6h4 c 0.6h5 5.

Evaluate each expression. See Example 2 and 3. x2 x 1 for a. x  2 b. x  3 x

Evaluate each expression. See Example 2 and 3. x2 x 7 for a. x  6 b. x  2

Evaluate each expression. See Example 2 and 3. 4t2 2t 8 x for a. t  1 s b. t  0

Evaluate each expression. See Example 2 and 3. 3s 2 2s 8 2 for a. s  1 b. s  0

Evaluate each expression. See Example 2 and 3. 1 2 a2 1 4 a for a. a  4 b. a  8 b

Evaluate each expression. See Example 2 and 3. 1 3 b2 1 9 b for a. b  9 b. b  9

Evaluate each expression. See Example 2 and 3. 9.2x x 6.5 2 x 1.4 5.4 for a. x  1 x b. x  2 x

Evaluate each expression. See Example 2 and 3. 10.3x 2x 6.5 2 for a. x  1 x b. x  2 x

Evaluate each expression. See Example 2 and 3. x 3 3x 2 2x 4 x  for a. x  2 b. x  2 x

Evaluate each expression. See Example 2 and 3. x 3 3x 2 x x 9 3 for a. x  3 b. x  3

Evaluate each expression. See Example 2 and 3. y y 1 4 y3 y 2 2y 1 x  2 for a. y  1 y b. y  1 y

Evaluate each expression. See Example 2 and 3. y 4 y 3 y 2 y y 1 4 y3 for a. y  1 y b. y  1 y

Evaluate each polynomial for a = -2 and b= 3 . See Example 4. 6a2b

Evaluate each polynomial for a = -2 and b= 3 . See Example 4. 4ab2 6

Evaluate each polynomial for a = -2 and b= 3 . See Example 4. a3 b3

Evaluate each polynomial for a = -2 and b= 3 . See Example 4. a3 b3 a

Evaluate each polynomial for a = -2 and b= 3 . See Example 4. a2 5ab b2a

Evaluate each polynomial for a = -2 and b= 3 . See Example 4. a3 2ab b3 a2

Evaluate each polynomial for a = -2 and b= 3 . See Example 4. 5ab3 ab b 10 a3 2

Evaluate each polynomial for a = -2 and b= 3 . See Example 4. ab3 ab a 21 3 a

Construct a table of solutions and then graph the equation. See Examples 57. y  x 4 2 1 a3

Construct a table of solutions and then graph the equation. See Examples 57. y  x2 4

Construct a table of solutions and then graph the equation. See Examples 57. y  x 2 2 y

Construct a table of solutions and then graph the equation. See Examples 57. y  x 1 2 2

Construct a table of solutions and then graph the equation. See Examples 57. y  2x 2 2 3 y

Construct a table of solutions and then graph the equation. See Examples 57. y  2x 2 y  2x 2 2

Construct a table of solutions and then graph the equation. See Examples 57. y  x 4 3 2 y

Construct a table of solutions and then graph the equation. See Examples 57. y  x 3 y  x 4 3

Construct a table of solutions and then graph the equation. See Examples 57. y  x 2 3 3 y

Construct a table of solutions and then graph the equation. See Examples 57. y  x 3 y  x 2 3

Construct a table of solutions and then graph the equation. See Examples 57. y  x 3 1 y

Construct a table of solutions and then graph the equation. See Examples 57. y  x3 y

Supermarkets. A grocer plans to set up a pyramid-shaped display of cantaloupes like that shown in Example 3. If each side of the square base of the display is made of six cantaloupes, how many will be used in the display?

Packaging. The polynomial 4x3 44x2 120xy gives the volume (in cubic inches) of the resulting box when a square with sides inches long is cut from each corner of a 10 in. 12 in. piece of cardboard. Find the volume of a box if 3-inch squares are cut out. Fold on dashed lines. x x x x x x x

Stopping Distance. The number of feet that a car travels before stopping depends on the drivers reaction time and the braking distance, as shown in the illustration. For one driver, the stopping distance is given by the polynomial 0.04v2 0.9v where is the velocity of the car. Find the stopping distance when the driver is traveling at 30 mph. Decision to stop 30 mph Reaction time Braking distance Stopping distance d

Suspension Bridges. The following polynomial 0.0000001s4 0.0066667s 2 400 8approximates the length of the cable between the two vertical towers of a bridge, where is the sag in the cable (in feet). Estimate the length of the cable if the sag is 24.6 feet. 400 ft

Sound Engineering Technician Many people in the recording industry have been impressed by the success of Apples iTunes Music Store. The polynomial 0.32x2 0.36x 0.218 approximates the number of song downloads from iTunes. When , the polynomial estimates the number of downloads (in billions) as of January 2004. When , it estimates the number of downloads (in billions) as of January 2005, and so on. Suppose the trend continues. Use the polynomial to estimate the number of iTunes downloads as of January 2014. (Source: eagereyes.org)

Twitter. When x  1, the polynomial 4.4x2 36.2x 42.5y approximates the number of Tweets (in millions) on the social network Twitter for January, 2009. When x  2, it approximates the number of Tweets (in millions) for the month of February, 2009, and so on. Use the polynomial to find the number of Tweets (in millions) for the month of October, 2009. (Source: pingdom.com)

Science History. The Italian scientist Galileo Galilei (15641642) built an incline plane like that shown to study falling objects. As the ball rolled down, he measured the time it took the ball to travel different distances. Graph the data and then connect the points with a smooth curve. Seconds Distance traveled 0 1 1 1 4 1 4 1 1 2 1 2 1

Dolphins. At a marine park, three trained dolphins jump in unison over an arching stream of water whose path can be described by the equation y  0.05x2 2x3. Given the takeoff points for each dolphin, how high must each jump to clear the stream of water? y x 15 ft 20 ft 30 ft Water level Take-off points for dolphins

Describe how to determine the degree of a polynomial.

List some words that contain the prefixes mono, bi, or tri.

To graph y  x2 4, a table of solutions is constructed and a graph is drawn. Explain the error. y  x2 4 0 2 0 (2, 0) 4 (0, 4) yx (x, y) x y (2, 0) (0, 4) 11 1 1 2 3 4 5 2 3 234

The expression x + y is a binomial. Is also a binomial? Explain.

Solve each inequality. Write the solution set in interval notation and graph it. 4(3y 2)  28 5

Solve each inequality. Write the solution set in interval notation and graph it. 5  3t 4  13x

Simplify each expression. Do not use negative exponents in the answer. (x 2 x4 ) 3

Simplify each expression. Do not use negative exponents in the answer. (a2 ) 3 (a3 ) 2

Simplify each expression. Do not use negative exponents in the answer. y 2 y 5 y 4 b 3

Simplify each expression. Do not use negative exponents in the answer. a 2t 3 t b 4

Find a three-term polynomial of degree 2 whose value will be 1 when it is evaluated for x = 2.

Graph: y  2x 3 3x 2 11x 6 x 

( b3 b2 9b 1) (b3 b2 9b 1) is the sum of two ______.

(b2 9b 11) (4b2 19b) is the ______ of a trinomial and a binomial.

_______ terms have the same variables with the same exponents.

The polynomial 2t4 3t3 4t2 5t 6 is written in powers of .t

To add polynomials, ______ their like terms.

To subtract polynomials, _____ the signs of the terms of the polynomial being subtracted, drop parentheses, and combine like terms.

Simplify each polynomial, if possible. a. 2x2 3x2 b. 15m3 m3 2 c. 8a d 3 b a3b b. 6cd 4c2 d 3

What is the result of the addition in the x-column? 4x2 x 12 x 5x 2 8x 23 4

Write without parentheses. a. (5x 7) 2 8x 23)5x b. (5y4 3y2 (5x 7) 2 8

What is the result of the subtraction in the -column? 4x 2 (4x 6x 9 2 6x 9) 8x2 8x 7x

Fill in the blanks to add (subtract) the polynomials. 6x 2 2x 3) (4x 2 7x 1) 4x (6x 2 ) ( 7x) (3 ) (6x  5x

Fill in the blanks to add (subtract) the polynomials. (6x 2 2x 3) (4x 2 7x 1)  5 6x2 2x 3 4x2 7x 1 (6x  9x

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 8t 2 4t 2

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 15x2 10x 2 8

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 18x 2 19x 2x2 1

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 17y 2 22y y 2 18

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 10x 7y 2 8x 9x 9x 2 17y

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 3y 2 y 6y 2 10x 7y 2 8

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 5 x 2 3 8 x 2 3 x 2 1 4 x 5.

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 7 y 2 1 2 y 2 3 y 2 1 5 y 1

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 0.6x 3 0.8x 4 0.7x 3 (0.8x 4 ) 6

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 1.9m4 2.4m6 3.7m4 2.8m6 0.

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 1 2 st 3 2 st

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 2 5 at 1 5 at

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 4ab 4ab ab xy

Simplify each polynomial and write it in descending powers of one variable. See Example 1. xy 4xy 2xy2

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 4x 2 y 5 6x 3 y 3x 2 y 2x 3 y 4ab

Simplify each polynomial and write it in descending powers of one variable. See Example 1. 5b 9ab2 10a3 b 8ab2 9a3 b 4x

Add the polynomials. See Example 2. (3q2 5q 7) (2q2 q 12)

Add the polynomials. See Example 2. 2t 2 11t 15) (5t 2 13t 10) (3q2

Add the polynomials. See Example 2. a 2 3 y3 3 4 y 2 1 2 b a 1 3 y3 1 5 y 2 1 6 b (2t

Add the polynomials. See Example 2. a 1 16 r 6 1 2 r 3 11 12b a 9 16 r 6 9 4 r 3 1 12b a 2

Add the polynomials. See Example 2. (0.3p 2.1q) (0.4p 3q)

Add the polynomials. See Example 2. (0.3r 5.2s) (0.8r 5.2s)

Add the polynomials. See Example 2. (2x2 xy 3y2 ) (5x 2 y 2 ) (0.

Add the polynomials. See Example 2. (4a2 ab 15b2 ) (5a2 b2 ) (2x2

Find a polynomial that represents the perimeter of the figure. See Example 3. (x2 + 3x + 1) yd (x2 4) yd

Find a polynomial that represents the perimeter of the figure. See Example 3. (5y5 5y3) inches (y5 + y3) inches (2

Find a polynomial that represents the perimeter of the figure. See Example 3. + 6) mi (x + 6) mi (5x2 + 3x + 1) mi

Find a polynomial that represents the perimeter of the figure. See Example 3. (11a2 5a + 1) ft (5a2 (4a 6a) ft 2 + 1) ft (9a

Use vertical form to add the polynomials. See Example 4. 2x 12 2 3x 6 6x 3 4x 2 3x 7

Use vertical form to add the polynomials. See Example 4. 7x 3 9x 2 2x 12 2 3x 6 6x 3

Use vertical form to add the polynomials. See Example 4. 6a 3c 5 2 7a 9 9a 1 2 2 2

Use vertical form to add the polynomials. See Example 4. 2c 2 6a 3c 5 2 14c 2 9a 1 2

Use vertical form to add the polynomials. See Example 4. z 3x 5 3 6z 2 7z 16 14c 9z x 7 3 6z 2 8z 18 3x 3

Use vertical form to add the polynomials. See Example 4. 3x 3 4x 2 z 3x 5 3 3x 3 4x 2 9z x 7 3

Use vertical form to add the polynomials. See Example 4. 3x 4xy 25 3 y 2 4x 2 y 4x 9 3x 3 2x 12 3 y 2 9x 3 3x

Use vertical form to add the polynomials. See Example 4. 3x 2 y 2 3x 4xy 25 3 5x 2 y 2 2x 12 3

Subtract the polynomials. See Example 5. (3a2 2a 4) (a2 3a 7)5x

Subtract the polynomials. See Example 5. (2b2 3b 5) (2b2 4b 9) (3a2

Subtract the polynomials. See Example 5. (4h3 5h2 15) (h3 15) (2b2

Subtract the polynomials. See Example 5. (c5 5c4 12) (2c5 c4) (4h3

Subtract the polynomials. See Example 5. 3 8 s 8 3 4 s 7 b a 1 3 s 8 1 5 s 7 b (c

Subtract the polynomials. See Example 5. a 5 6 q9 4 5 q8 b a 1 4 q9 3 8 q8 b

Subtract the polynomials. See Example 5. (5ab 2b2) (2 ab b2) a

Subtract the polynomials. See Example 5. (mn 8n2 ) (6 5mn n2) (5a

Use vertical form to subtract the polynomials. See Example 6. Subtract 2x2 2x 3 from 5 2 2x 3

Use vertical form to subtract the polynomials. See Example 6. Subtract 3y 4y 13 2 from 6y 7 3x2

Use vertical form to subtract the polynomials. See Example 6. Subtract (s 9) 2 4s 2) 6y2 from (5s 2 (s 9) 2

Use vertical form to subtract the polynomials. See Example 6. Subtract (4p 30) 2 4p 40) (5 from (10p2 (4p 30) 2

Use vertical form to subtract the polynomials. See Example 6. Subtract 8a 10 3 8a2 3a 1 from 17a3 8a 25a 10 3.

Use vertical form to subtract the polynomials. See Example 6. Subtract from . m m 22 3 20m2 15m 39 17a3 from 4m3 m m 22 3

Use vertical form to subtract the polynomials. See Example 6. 0.2x 3 1.2x 2 3.6x 0.9) 0.8x 3

Use vertical form to subtract the polynomials. See Example 6. (6.3y3 4.4y 2 2.7y 8.8) 9.7y

Perform the operations. See Example 7. Subtract (3x 7x 1) 2 4x 7) from the sum of (2x2 (3x 7x 1) 2 and (4x2 8x 7).

Perform the operations. See Example 7. Subtract (32x 2 17x 45) from the sum of (23x 12x 7) and (11x2 12x 7) 2

Perform the operations. See Example 7. Subtract t 3 2t 2 2 from the sum of 3t 3 t 2 t and t 3 6t 3 3t

Perform the operations. See Example 7. Subtract 3z 3z 7 3 4z 7 t 3 from the sum of 2z 2 3z 3z 7 3 and 4z . 3 2z 32.

Perform the operations. (9a 3a) (2a 4a2)

Perform the operations. (4b2 3b) (7b b2)

Perform the operations. Subtract (y5 5y4 1.2) from (2y5 y4)

Perform the operations. Subtract (4w3 5w2 7.6) from (w3 15w2)

Perform the operations. 3r 4r 7r4

Perform the operations. 2b4 7b 3b4

Perform the operations. 0.03f2 0.25f 0.91 (0.17f2 1.18)

Perform the operations. 0.05r 2 0.33r) (0.48 r 2 0.15r 2.14) (0.

Perform the operations. a 7 8 r 4 5 9 r 2 9 4 b a3 8 r 4 2 3 r 2 1 4 b (0.05

Perform the operations. a 4 5 t 4 1 3 t 2 1 2 b a1 2 t 4 3 8 t 2 1 16b a 7

Perform the operations. (c 8t 2 2 2c 9) 3t 3 4t 2 8c 3t 5

Perform the operations. 1t 3 (c 8t 2 2 2c 9) 3t 3 4t

Perform the operations. (12.1h3 9.9h2 ) (7.3h3 1.1h2 ) 11

Perform the operations. (5.7n3 2.1n) (6.2n3 3.9n) (12

Perform the operations. (20 4rt 5r 2 t) (10 5rt) (5.

Perform the operations. (5m2 8m 8) (20m2 m) (20

Perform the operations. (3x 2 3x 2) (3x 2 4x 3) (5m2

Perform the operations. (4c 2 3c 2) (3c 2 4c 2) (3x

Perform the operations. 2 3 d2 1 4 c 2 5 6 c 2 1 2 cd 1 3 d2 (4c

Perform the operations. 3 5 s 2 2 5 t 2 1 2 s 2 7 10 st 3 10 st 2

Perform the operations. (3x 7) (4x 3) 3

Perform the operations. (2y 3) (4y 7) (3x

Perform the operations. Subtract 1.7t 2.1t 1.7 2 1.1t from the sum of 2.7t 2 1.7t 2.1t 1.7 2 and 3.1t 2 2.5t 2.3 2.

Perform the operations. Subtract 1.07x 5.01 2 2.07x 3 from the sum of 1.04x 2 1.07x 5.01 2 and 1.33x 1.9x 2 5.02 1

Perform the operations. 32u3 16u3

Perform the operations. 25x 3 7x 3 32

Perform the operations. (9d2 6d) (8d 4d2)

Perform the operations. (2c 2 4c) (8c c 2 ) (9d

Perform the operations. x3 y2 4x 2 y 7x 12 (4x 3 y2 6x 2 y 9x 3) 3x3

Perform the operations. 2x 2 y 2 12y 2 (10x 2 y 2 9xy 24y 2 )

Perform the operations. (2x 2 3x 1) (4x 2 3x 2) (2x 2 3x 2) (10x 2

Perform the operations. (3z 2 4z 7) (2z 2 2z 1) (2z 2 3z 7) 108. Read

Perform the operations. 4x m 3 4x 2 3x 10 (3z (5x m) 3 2x2 4x 4) 7m5

Perform the operations. 7m5 m3 9m2 4x m 3 (8m5 2m3 m2 (5x m) 3 2x

Perform the operations. a. (8x2 3x) (11x2 6x 10) b. (8x2 3x) (11x 2 6x 10)

Perform the operations. a. (10 2st 3s 2 t) (4 6st) b. (10 2st 3s 2 t) (4 6st) (1

Greek Architecture. a. Find a polynomial that represents the difference in the heights of the columns. b. If the columns were stacked one atop the other, to what height would they reach? (x2 3x + 2) ft (5x 10) ft

Jets. Find a polynomial that represents the length of the larger jet.

Piatas. Find a polynomial that represents the length of the rope used to hold up the piata. 2a2 6 inches 4a2 + 6a 1inches

Reading Blueprints. Find a polynomial that represents a. the difference in the length and width of the one-bedroom apartment. b. the perimeter of the apartment. (x2 x + 6) ft Length Width (4x + 3) ft Dining Area Bedroom Closet Lin. Bath La

Naval Operations. Two warning flares are fired upward at the same time from different parts of a ship. The height of the first flare is (16t2 128t 20) feet and the height of the higher-traveling second flare is (16t2 150t 40) (16feet, after seconds. a. Find a polynomial that represents the difference in the heights of the flares. b. In 4 seconds, the first flare reaches its peak, explodes, and lights up the sky. How much higher is the second flare at that time?

Auto Mechanics. The length of a fan belt that wraps around three pulleys is (3x2 11x 4.5p)t in. Find a polynomial that represents the unknown length of a part of the belt shown in the illustration below. 2 1.5 x ? 2 + 5x x2

How do you recognize like terms?

Explain why the vertical form used in algebra to add 2x 3x 6 2 4x 3116 and 5x2 2x 3x 6 2 is similar to the vertical form used in arithmetic to add 243 and 536.

Explain the error below. 7x 2 y 6x 2 y  13x 4 y 2 5

Explain the error below. 12x2 4) (3x2 1)  12x2 4 3x2 1 7x 2

A student was asked to simplify 1 6 x 2 3 2 3 x 2. Explain the error below: 6a 1 6 x2 3 2 3 x2 b  x2 18 4x2  5x2 18

Explain the error below. Subtract (2d 9) 2 d 3) and (d2 (2d 9) (2d2 d 3) (d2 9)  d2 d 6 (d2 (

What is the sum of the measures of the angles of a triangle?

What are the formulas for the area of a circle and the area of a triangle?

Graph: y  1 2 x 2 (2

Graph: 2x 3y  9

What polynomial must be added to 2x 2 x 3 y so that the sum is 6x2 7x 8?

Is the sum of two trinomials always a trinomial? Explain why or why not.

(2x 3 )(3x 4 ) is the product of two _____ and (2a 4)(3a 5) is the product of two ______ .

We read (x 7)(2x 3) x as the ____ of the quantity of x 7 _____ the quantity of 2x 3.

In the acronym FOIL, F stands for _____ terms, O for _____ terms, I for ____ terms, and L for ____terms.

(2a 4)(3a2 5a 1) is the product of a _____ and a ____.

a. To multiply two polynomials, multiply _____ term of one polynomial by _____ term of the other polynomial, and then combine like terms. b. When multiplying three polynomials, we begin by multiplying _____ two of them, and then we multiply that result by the _____ polynomial.

Label each arrow using one of the letters F, O, I, or L. Then fill in the blanks. First Outer Inner Last

Simplify each polynomial by combining like terms. a. 6x 2 8x 9x 12 b. 5x4 3ax2 5ax2 3a26x

(3a)(2a2) can be classified as a monomial  monomial. Classify the following products by identifying the types of polynomial factors. a. b. c. d. 6m(m2 1)(m2 1) (c d)(c 2 c d) (9a 1)(5a 3) 6x(x 7) (3a)(2a2

Complete each solution. (9n3) (8n2) (9 n2

Complete each solution. 7x (3x2 2x 5) (3x2) (2x) (5) 6x2 10 6x2 10

Complete each solution. 6x2 10  6x2 10 (2x 5)(

Complete each solution. 17x 2 6 6x 3 8x 2 4x 12x 6 2x 3 3x 2 4x

Multiply. See Example 1. 5m  m

Multiply. See Example 1. 4s  s

Multiply. See Example 1. (3x ) 2 )(4x 3 )

Multiply. See Example 1. (2a3 )(11a2 (3x ) 2

Multiply. See Example 1. (1.2c ) 3 )(5c3 )

Multiply. See Example 1. (2.5h4 )(2h4 (1.2c ) 3

Multiply. See Example 1. (3b ) 2 )(2b)(4b3 )

Multiply. See Example 1. (3y)(7y 2 )(y 4 (3b ) 2

Multiply. See Example 1. 2x ) 2 y 3 )(4x 3 y 2

Multiply. See Example 1. (5x 3 y 6 )(2x2 y 2 (2x ) 2

Multiply. See Example 1. 8a ) 5 )a1 4 a6 b

Multiply. See Example 1. a2 3 x 6 b(9x 3 (8a ) 5

Multiply. See Example 2. 3x(x 4) 3

Multiply. See Example 2. 3a(a 2)

Multiply. See Example 2. 4t(t 3) 2 7) 3x

Multiply. See Example 2. 6s(s 2 4t(t 3) 2

Multiply. See Example 2. 2x 2b 2) 3 (3x 2 x 1) 6s(s

Multiply. See Example 2. 4b3 (2b2 2x 2b 2) 3 (

Multiply. See Example 2. 5 8 t 2 (t 6 8t 2 ) 4

Multiply. See Example 2. 4 9 a2 (9a3 a2 ) 5

Multiply. See Example 2. 4x 2 z(3x 2 z 2 xz 1) 4 9

Multiply. See Example 2. 3x 2 y(x 2 y 2 xy 1) 4x

Multiply. See Example 2. (x ) 2 12x)(6x12)

Multiply. See Example 2. (w9 11w)(2w7 (x ) 2

Find a polynomial that represents the area of the parallelogram or rectangle. See Example 3. (7h + 3) in. h

Find a polynomial that represents the area of the parallelogram or rectangle. See Example 3. (8h 8) in. h

Find a polynomial that represents the area of the parallelogram or rectangle. See Example 3. (4w 2) ft w ft

Find a polynomial that represents the area of the parallelogram or rectangle. See Example 3. (8w + 1) yd w yd

Multiply. See Examples 4 and 5. (y 3)(y 5)

Multiply. See Examples 4 and 5. (a 4)(a 5)

Multiply. See Examples 4 and 5. (m 6)(m 9)

Multiply. See Examples 4 and 5. (n 8)(n 10)

Multiply. See Examples 4 and 5. (4y 5)(y 7) (3

Multiply. See Examples 4 and 5. (3x 4)(x 5)

Multiply. See Examples 4 and 5. (2x 3)(6x 5)

Multiply. See Examples 4 and 5. (5x 3)(2x 3)

Multiply. See Examples 4 and 5. (3.8y 1)(2y 1)

Multiply. See Examples 4 and 5. (2.6x 3)(2x 1)

Multiply. See Examples 4 and 5. a6m b 2 3 b a3m 4 3 b (

Multiply. See Examples 4 and 5. a8t 1 2 b a4t 5 2 a6m b 2

Multiply. See Examples 4 and 5. (t 8) 2 3)(t 2 4) a8

Multiply. See Examples 4 and 5. (s 3 6)(s 3 (t 8) 2

Multiply. See Examples 4 and 5. (3a 2b)(4a b) (2

Multiply. See Examples 4 and 5. 2t 3s)(3t s)

Multiply. See Example 6. (x 2)(x 2 2x 3)

Multiply. See Example 6. (x 5)(x 2 2x 3)

Multiply. See Example 6. (4t 3)(t 2 2t 3)

Multiply. See Example 6. (3x 1)(2x 2 3x 1)

Multiply. See Example 6. (x 2 6x 7)(2x 5)

Multiply. See Example 6. (y 2 2y 1)(4y 8)

Multiply. See Example 6. (r 2 r 3)(r 2 4r 5)

Multiply. See Example 6. (w2 w 9)(w2 w 3)

Multiply using vertical form. See Example 7. x r 6 2 2x 1 (w2

Multiply using vertical form. See Example 7. 5r 2 x r 6 2

Multiply using vertical form. See Example 7. 4x x 1 2 3x 4 x

Multiply using vertical form. See Example 7. x 2 4x x 1 2

Multiply. See Example 8. 4x(2x 1)(x 2) 3

Multiply. See Example 8. 5a(3a 2)(2a 3) 4

Multiply. See Example 8. 3a(a b)(a b) 5a

Multiply. See Example 8. 2r(r s)(r s) 3a

Multiply. See Example 8. (2a2 )(3a3 )(3a 2) 2r

Multiply. See Example 8. (3x)(2x2 )(x 4)

Multiply. See Example 8. (x 4)(x 1)(x 3)

Multiply. See Example 8. (x 6)(x 2)(x 4)

Multiply (5x 2)(6x 1) (8

Multiply (8x 1)(3x 7)

Multiply (3x ) 2 4x 7)

Multiply (2y 2 7y 8)(3y 3 (3x ) 2

Multiply 2(t 4)(t 3) 8

Multiply 4(x 7)(x 6)

Multiply 3a 4y 3 2 2a 4 3y 2 2a 2y

Multiply y 2 3a 4y 3 2 2a 4 3y 2

Multiply (t 2s)(9t 3s) (4

Multiply (4t u)(3t u)

Multiply a ) 1 2 ab(4a4 )(a5

Multiply (12b)a 7 6 bb(b4 a )

Multiply a4a tb 5 4 rb a4a 3 4 rb

Multiply 5c 2 5 tb a10c 1 5 a4a tb 5

Multiply (a b)(a b) (m

Multiply (m n)(m n)a

Multiply (x 6)(x 3 5x 2 4x 4) (a

Multiply (x 8)(x 3 4x 2 2x 2) (x

Multiply 9x 5y 10) 2 (x 2 2x 6) (x

Multiply 4y 2 (y 2 9x 5y 10) 2

Multiply 4y(y 3)(y 7) 2t

Multiply 2t(t 8)(t 10)4

Multiply 0.3p ) 5 (0.4p4 6p2

Multiply 0.5u5 (0.4u6 0.5u3 0.3p ) 5

Multiply 8.2pq(2pq 3p 5q) 5.

Multiply 5.3ab(2ab 6a 3b)

Multiply (3x y)(x 2 8xy 16y 2 ) 8.2

Multiply (3x y)(x 2 3xy y 2

Perform the indicated operations to simplify each expression, if possible. a. (x 2) (x 2x 4) 2 2x 4) b. (x 2)(x 2 (x 2) (x 2x 4) 2 2x

Perform the indicated operations to simplify each expression, if possible. a. (a 3) (a 3a 9) 2 3a 9) b. (a 3)(a2 (a 3) (a 3a 9) 2 3a

Perform the indicated operations to simplify each expression, if possible. a. (6x ) 2 z 5 ) (3xz3 b. (6x 2 z 5 )(3xz3 (6x ) 2

Perform the indicated operations to simplify each expression, if possible. a. (5r t) 4 t 2 ) (2r 2 t) b. (5r 4 t 2 )(2r 2 (5r t) 4

Perform the indicated operations to simplify each expression, if possible. a. (2x 3x) 2 x) (3x2 3x) b. (2x2 x)(3x2 (2x 3x) 2

Perform the indicated operations to simplify each expression, if possible. a. (4.9a b) (2a b) b. (4.9a b)(2a b)

Perform the indicated operations to simplify each expression, if possible. a. 3a (4a 1) (6a 2) b. 3a(4a 1)(6a 2)

Perform the indicated operations to simplify each expression, if possible. a. a c db 1 2 c 3db a 3 4 c db 3a b. a 1 2 c 3db a3 4 a c db 1

Stamps. Find a polynomial that represents the area of the stamp.

Parking. Find a polynomial that represents the total area of the van-accessible parking space and its access aisle. x 2x ft + 10) ft

Sunglasses. An ellipse is an oval-shaped curve. The area of an ellipse is approximately 0.785lw, where l is its length and w is its width. Find a polynomial that represents the approximate area of one of the elliptical-shaped lenses of the sunglasses. 1) in. (x + 1) in.

Gardening. Refer to the illustration below. a. Find the area of the region planted with corn, tomatoes, beans, and carrots. Add your answers to find the total area of the garden. b. Find the length and width of the garden. Multiply your answers to find its area. c. How do the answers from parts (a) and (b) for the area of the garden compare? x ft x ft 5 ft 6 ft Corn Beans Carrots T o m a t o e s

Luggage. Find a polynomial that represents the volume of the garment bag. (Recall that the formula for the volume of a rectangular solid is .) (2x + 2) in. (x 3) in. x in

Baseball. Find a polynomial that represents the volume within the batting cage. 3x + 1) ft (5x + 3) ft (3x 2) ft

Is the product of a monomial and a monomial always a monomial? Explain.

Explain this diagram. 5x 6)(7x 1)

Explain why the FOIL method cannot be used to find (3x 2)(4x 2 x 10)

Explain the error: x 3)(x 2)  x2 6

Explain why the vertical form used in algebra to multiply 2x 3x 2 2 and 3x 2 2 is similar to the vertical form used in arithmetic to multiply 231 and 32.

Would the OLIF method give the same result as the FOIL method when multiplying two binomials? Explain why or why not.

What is the slope of a. Line 1? c. Line 3? b. Line 2? d. the -axis? x y Line 3 Line 1 Line 2 111 1 2 3 4 2 3 4 234 3 4

a. What is the -intercept of Line 1? b. What is the -intercept of Line 1? Line 3 Line 1 Line 2 111 1 2 3 4 2 3 4 234 3 4

a. Find each of the following products. i. ii. iii. b. Write a product of two polynomials such that the result is x 5 1 (x 1)(x 3 x 2 x 1) (x 1)(x 2 x 1) (x 1)(x 1) x y x y L

Solve: (y 1)(y 6)  (y 3)(y 2) 8 x

Expressions of the form (x  y)2, and occur so frequently in algebra that they are called special ________.

(2x  3) is the_____of a binomial and (a  6)(a 6 ) is the product of the sum and difference of the ____ two terms.

Fill in the blanks to describe each special product. a. x  y) 2 x 2  2xy  y 2 The ____ of the second term the ____ product of the first and second terms The square of the ____ term b. (x  y)(x y) x 2 y2 (x The square of the _____ term . The of the first term

Consider the binomial 5x  4. a. What is the square of its first term? b. What is twice the product of its two terms? c. What is the square of its second term?

Complete each solution to find the product. (x  4)2 2  2(x)( )  2 x2   16

Complete each solution to find the product. (6r 1)2 ( ) 2 2(6r)(1)  (1)2 x

Complete each solution to find the product. (s  5)(s 5) 2 2

True or false: (t  7)(t 7) (t 7)(t  7)?

Find each product. See Example 1. (x  1)2

Find each product. See Example 1. (y  7)2

Find each product. See Example 1. (m 6)2

Find each product. See Example 1. (b 1)2 (

Find each product. See Example 1. (4x  5)2

Find each product. See Example 1. (6y  3)2

Find each product. See Example 1. (7m 2)2

Find each product. See Example 1. (9b 2)2 (

Find each product. See Example 1. (1 3y) 2

Find each product. See Example 1. (1 4a) 2

Find each product. See Example 1. y  0.9)2

Find each product. See Example 1. (d  0.2)2

Find each product. See Example 1. (a2  b2 ) 2

Find each product. See Example 1. (c 2  d2 ) 2

Find each product. See Example 1. as  3 4 b 2

Find each product. See Example 1. ay 5 3 b 2 a

Find each product. See Example 2. (x  3)(x 3) (

Find each product. See Example 2. (y  6)(y 6)

Find each product. See Example 2. (2p  7)(2p 7) (

Find each product. See Example 2. (5t  4)(5t 4)

Find each product. See Example 2. (3n  1)(3n 1) (

Find each product. See Example 2. 5a  4)(5a 4)

Find each product. See Example 2. ac  b 3 4 b ac 3 4 b

Find each product. See Example 2. am  4 5 b am 4 5 ac  b 3

Find each product. See Example 2. (0.4 9m ) 2 )(0.4  9m2 ) a

Find each product. See Example 2. (0.3 2c 2 )(0.3  2c 2 (0

Find each product. See Example 2. (5 6g)(5  6g) )

Find each product. See Example 2. (6 c 2 )(6  c

Expand each binomial. See Example 3. (x  4)3

Expand each binomial. See Example 3. (y  2)3 (

Expand each binomial. See Example 3. (n 6)3

Expand each binomial. See Example 3. (m 5)3 (n

Expand each binomial. See Example 3. 2g 3)3

Expand each binomial. See Example 3. (3x 2)3 (

Expand each binomial. See Example 3. (a  b) 3

Expand each binomial. See Example 3. (c d) 3

Perform the operations. See Example 4. 2(x 2  7x 1) 3(x 2 2x  2) (c

Perform the operations. See Example 4. 2t(t  2)  (t 1)(t  9)

Perform the operations. See Example 4. (3x  4)(2x 2) (2x  1)(x  3) 2t

Perform the operations. See Example 4. (5a 1)2 (a 8)(a  8) (3

Perform the operations. See Example 4. 5d(4d 1)2 (5

Perform the operations. See Example 4. 2h(7h 2)2 5d

Perform the operations. See Example 4. 4d(d ) 2  g3 )(d2 g3

Perform the operations. See Example 4. 8y(x 2  y 2 )(x 2 y 2 4d(d )

Find a polynomial that represents the area of the figure. Leave p in your answer. See Example 5. (2x 2) yd (2x + 2) yd

Find a polynomial that represents the area of the figure. Leave p in your answer. See Example 5. (3x 4) cm (3x + 4) cm

Find a polynomial that represents the area of the figure. Leave p in your answer. See Example 5. (3x + 1) ft (3x + 1) ft

Find a polynomial that represents the area of the figure. Leave p in your answer. See Example 5. (x 3) in.

Perform the operations. (2v 3 8)2

Perform the operations. (8x 4 3)2 (

Perform the operations. 3x(2x  3)(2x  3)

Perform the operations. 4y(3y  4)(3y  4)

Perform the operations. (4  0.4)(4 0.4) (

Perform the operations. 4t  0.6)(4t 0.6)

Perform the operations. (r 2  10s) 2

Perform the operations. (m2  8n) 2

Perform the operations. 2(x  3)  4(x 2) 3

Perform the operations. 3(y 4) 5(y  3)

Perform the operations. ad4  1 4 b 2

Perform the operations. aq6  1 3 b 2

Perform the operations. (d  7)(d 7) (t

Perform the operations. (t  2)(t 2)

Perform the operations. (2a 3b) 2

Perform the operations. (2x  5y) 2

Perform the operations. (n  6)(n 6) (a

Perform the operations. (a  12)(a 12)

Perform the operations. (m  10)2 (m 8)2

Perform the operations. (5y 1)2 (y  7)(y 7)

Perform the operations. 2m  n) 3

Perform the operations. p 2q) 3

Perform the operations. a5m 6 5 b 2

Perform the operations. a6m 7 6 b 2

Perform the operations. (r 2 s 2 ) 2

Perform the operations. (t 2 u2 ) 2 (

Perform the operations. (x 2)2

Perform the operations. (a  2)2

Perform the operations. (r  2)2

Perform the operations. (n  10)2

Perform the operations. (n 2)4

Perform the operations. (c  d) 4

Perform the operations. 5(y 2 2y 6)  6(2y 2  2y 5) (c

Perform the operations. (4b  1)2 (b 7)(b  7) 5

Perform the operations. (3x 2)2  (2x  1)2

Perform the operations. (4a 3)2  (a  6)2

Perform the operations. ( 8)2

Perform the operations. (w 9)2 (

Perform the operations. a6b  b 1 2 b a6b 1 2 b

Perform the operations. 6. 4h  2 3 b a4h 2 3 a

Perform the operations. 3y(y  2)  (y  1)(y 1)

Perform the operations. (x  y)(x y)  x(x  y)

Perform the operations. (6 2d3 ) 2 (

Perform the operations. (6 5p2 ) 2

Perform the operations. (2e  1)3

Perform the operations. (3m 2n) 3

Perform the operations. (8x  3)2

Perform the operations. (4b 8)2 (8

Perform the indicated operations. a. (xy)2 b. (x  y)2

Perform the indicated operations. a. (cd) b. (c d)2

Perform the indicated operations. a. (2b2 d) 2 b. (2b2  d) 2 (

Perform the indicated operations. a. (mn)3 b. (m  n)3

Playpens. Find a polynomial that represents the area of the floor of the playpen. (x + 6) in. (x + 6) in.

Storage. Find a polynomial that represents the volume of the cubicle. (x +5) in. (x +5) in. (x +5) in.

Paper Towels. The amount of space (volume) occupied by the paper on the roll of paper towels is given by the expression ph(R  r)(R r) , where is the outer radius and is the inner radius. Perform the indicated multiplication. h r R

Signal Flags. Refer to the illustration below. Find a polynomial that represents the area in blue of the maritime signal flag for the letter . The dimensions are given in centimeters. 4x + 1 3x + 2 4x + 1 x

What is a binomial? Explain how to square it.

Writing (x  y) 2 as x 2  y 2 illustrates a common error. Explain.

We can find (2x  3)2 and (5y 6)2 using the FOIL method or using special product rules. Explain why the special product rules are faster.

a. Fill in the blanks: (xy)2 is the _____ of a product and (x  y)2 is the _____ of a sum. b. Explain why (xy) . 2  (x  y) 2

Simplify: 30 36

Add: 5 12  1 4

Multiply: 7 8  3 5

Divide: 1 3  4 5