 5.2.1: To multiply the variables in monomials, retain each variable and __...
 5.2.2: To multiply 7x3 (4x5  8x2 + 6), use the ______________ property to...
 5.2.3: To multiply (5x + 3)(x2 + 8x + 7), begin by multiplying each term o...
 5.2.4: When using the FOIL method to find (x + 7)(3x + 5), the product of ...
 5.2.5: (A + B) 2 = ______________. The square of a binomial sum is the fir...
 5.2.6: (A  B) 2 = ______________. The square of a binomial difference is ...
 5.2.7: (A + B)(A  B) = ______________. The product of the sum and differe...
 5.2.8: If f(x) = x2  4x + 7, we find f(a + h) by replacing each occurrenc...
 5.2.9: 4x2 (3x + 2)
 5.2.10: 5x2 (6x + 7)
 5.2.11: 2y(y2  5y)
 5.2.12: 3y(y2  4y)
 5.2.13: 5x3 (2x5  4x2 + 9)
 5.2.14: 6x3 (3x5  5x2 + 7)
 5.2.15: 4xy(7x + 3y)
 5.2.16: 5xy(8x + 3y)
 5.2.17: 3ab2 (6a2b3 + 5ab)
 5.2.18: 5ab2 (10a2b3 + 7ab)
 5.2.19: 4x2y(3x4y2  7xy3 + 6)
 5.2.20: 3x2y(10x2y4  2xy3 + 7)
 5.2.21: 4xna3x2n  5xn + 1 2 xb
 5.2.22: 10xna4x2n  3xn + 1 5 xb
 5.2.23: (x  3)(x2 + 2x + 5)
 5.2.24: (x + 4)(x2  5x + 8)
 5.2.25: (x  1)(x2 + x + 1)
 5.2.26: (x  2)(x2 + 2x + 4)
 5.2.27: (a  b)(a2 + ab + b2 )
 5.2.28: (a + b)(a2  ab + b2 )
 5.2.29: (x2 + 2x  1)(x2 + 3x  4)
 5.2.30: (x2  2x + 3)(x2 + x + 1)
 5.2.31: (x  y)(x2  3xy + y2 )
 5.2.32: (x  y)(x2  4xy + y2 )
 5.2.33: (xy + 2)(x2y2  2xy + 4)
 5.2.34: (xy + 3)(x2y2  2xy + 5)
 5.2.35: (x + 4)(x + 7)
 5.2.36: (x + 5)(x + 8)
 5.2.37: (y + 5)(y  6)
 5.2.38: (y + 5)(y  8)
 5.2.39: (5x + 3)(2x + 1)
 5.2.40: (4x + 3)(5x + 1)
 5.2.41: (3y  4)(2y  1)
 5.2.42: (5y  2)(3y  1)
 5.2.43: (3x  2)(5x  4)
 5.2.44: (2x  3)(4x  5)
 5.2.45: (x  3y)(2x + 7y)
 5.2.46: (3x  y)(2x + 5y)
 5.2.47: (7xy + 1)(2xy  3)
 5.2.48: (3xy  1)(5xy + 2)
 5.2.49: (x  4)(x2  5)
 5.2.50: (x  5)(x2  3)
 5.2.51: (8x3 + 3)(x2  5)
 5.2.52: (7x3 + 5)(x2  2)
 5.2.53: (3xn  yn )(xn + 2yn )
 5.2.54: (5xn  yn )(xn + 4yn )
 5.2.55: (x + 3) 2
 5.2.56: (x + 4) 2
 5.2.57: (y  5) 2
 5.2.58: (y  6) 2
 5.2.59: (2x + y) 2
 5.2.60: (4x + y) 2
 5.2.61: (5x  3y) 2
 5.2.62: (3x  4y) 2
 5.2.63: (2x2 + 3y) 2
 5.2.64: (4x2 + 5y) 2
 5.2.65: (4xy2  xy) 2
 5.2.66: (5xy2  xy) 2
 5.2.67: (an + 4bn ) 2
 5.2.68: (3an  bn ) 2
 5.2.69: (x + 4)(x  4)
 5.2.70: (x + 5)(x  5)
 5.2.71: (5x + 3)(5x  3)
 5.2.72: (3x + 2)(3x  2)
 5.2.73: (4x + 7y)(4x  7y)
 5.2.74: (8x + 7y)(8x  7y)
 5.2.75: (y3 + 2)(y3  2)
 5.2.76: (y3 + 3)(y3  3)
 5.2.77: (1  y5 )(1 + y5 )
 5.2.78: (2  y5 )(2 + y5 )
 5.2.79: (7xy2  10y)(7xy2 + 10y)
 5.2.80: (3xy2  4y)(3xy2 + 4y)
 5.2.81: (5an  7)(5an + 7)
 5.2.82: (10bn  3)(10bn + 3)
 5.2.83: [(2x + 3) + 4y][(2x + 3)  4y]
 5.2.84: [(3x + 2) + 5y][(3x + 2)  5y]
 5.2.85: (x + y + 3)(x + y  3)
 5.2.86: (x + y + 4)(x + y  4)
 5.2.87: (5x + 7y  2)(5x + 7y + 2)
 5.2.88: (7x + 5y  2)(7x + 5y + 2)
 5.2.89: [5y + (2x + 3)][5y  (2x + 3)]
 5.2.90: [8y + (3x + 2)][8y  (3x + 2)]
 5.2.91: (x + y + 1) 2
 5.2.92: (x + y + 2) 2
 5.2.93: (x + 1)(x  1)(x2 + 1)
 5.2.94: (x + 2)(x  2)(x2 + 4)
 5.2.95: Let f(x) = x  2 and g(x) = x + 6. Find each of the following. a. (...
 5.2.96: Let f(x) = x  4 and g(x) = x + 10. Find each of the following. a. ...
 5.2.97: Let f(x) = x  3 and g(x) = x2 + 3x + 9. Find each of the following...
 5.2.98: Let f(x) = x + 3 and g(x) = x2  3x + 9. Find each of the following...
 5.2.99: f(x) = x2  3x + 7
 5.2.100: f(x) = x2  4x + 9
 5.2.101: f(x) = 3x2 + 2x  1
 5.2.102: f(x) = 4x2 + 5x  1
 5.2.103: (3x + 4y) 2  (3x  4y) 2
 5.2.104: (5x + 2y) 2  (5x  2y) 2
 5.2.105: (5x  7)(3x  2)  (4x  5)(6x  1)
 5.2.106: (3x + 5)(2x  9)  (7x  2)(x  1)
 5.2.107: (2x + 5)(2x  5)(4x2 + 25)
 5.2.108: (3x + 4)(3x  4)(9x2 + 16)
 5.2.109: (x  1) 3
 5.2.110: (x  2) 3
 5.2.111: (2x  7) 5 (2x  7) 3
 5.2.112: (5x  3) 6 (5x  3) 4
 5.2.113: In Exercises 113114, find the area of the large rectangle in two wa...
 5.2.114: In Exercises 113114, find the area of the large rectangle in two wa...
 5.2.115: In Exercises 115116, express each polynomial in standard formthat i...
 5.2.116: In Exercises 115116, express each polynomial in standard formthat i...
 5.2.117: In Exercises 117118, express each polynomial in standard form. a. W...
 5.2.118: In Exercises 117118, express each polynomial in standard form. a. W...
 5.2.119: A popular model of carryon luggage has a length that is 10 inches ...
 5.2.120: Before working this exercise, be sure that you have read the Blitze...
 5.2.121: Explain how to multiply monomials. Give an example.
 5.2.122: Explain how to multiply a monomial and a polynomial that is not a m...
 5.2.123: Explain how to multiply a binomial and a trinomial.
 5.2.124: What is the FOIL method and when is it used? Give an example of the...
 5.2.125: Explain how to square a binomial sum. Give an example.
 5.2.126: Explain how to square a binomial difference. Give an example.
 5.2.127: Explain how to find the product of the sum and difference of two te...
 5.2.128: How can the graph of function f g be obtained from the graphs of fu...
 5.2.129: Explain how to find f(a + h)  f(a) for a given function f.
 5.2.130: y1 = (x  2) 2 y2 = x2  4x + 4
 5.2.131: y1 = (x  4)(x2  3x + 2) y2 = x3  7x2 + 14x  8
 5.2.132: y1 = (x  1)(x2 + x + 1) y2 = x3  1
 5.2.133: y1 = (x + 1.5)(x  1.5) y2 = x2  2.25
 5.2.134: Graph f(x) = x + 4, g(x) = x  2, and the product function, f g, in...
 5.2.135: Knowing the difference between factors and terms is important: In (...
 5.2.136: I used the FOIL method to find the product of x + 5 and x2 + 2x + 1.
 5.2.137: Instead of using the formula for the square of a binomial sum, I pr...
 5.2.138: Specialproduct formulas have patterns that make their multiplicati...
 5.2.139: If f is a polynomial function, then f(a + h)  f(a) = f(a) + f(h) ...
 5.2.140: (x  5) 2 = x2  5x + 25
 5.2.141: (x + 1) 2 = x2 + 1
 5.2.142: Suppose a square garden has an area represented by 9x2 square feet....
 5.2.143: Express the area of the plane figure shown as a polynomial in stand...
 5.2.144: In Exercises 144145, represent the volume of each figure as a polyn...
 5.2.145: In Exercises 144145, represent the volume of each figure as a polyn...
 5.2.146: Simplify: (yn + 2)(yn  2)  (yn  3)2 .
 5.2.147: The product of two consecutive odd integers is 22 less than the squ...
 5.2.148: Solve: 3x + 4 10. (Section 4.3, Example 6)
 5.2.149: Solve: 2  6x 20. (Section 4.1, Example 2)
 5.2.150: Write in scientific notation: 8,034,000,000. (Section 1.7, Example 2)
 5.2.151: Replace each boxed question mark with a polynomial that results in ...
 5.2.152: (x  5)(x2 + 3)
 5.2.153: (x + 4)(3x  2y)
Solutions for Chapter 5.2: Multiplication of Polynomials
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 5.2: Multiplication of Polynomials
Get Full SolutionsIntermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Since 153 problems in chapter 5.2: Multiplication of Polynomials have been answered, more than 40363 students have viewed full stepbystep solutions from this chapter. Chapter 5.2: Multiplication of Polynomials includes 153 full stepbystep solutions.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.