Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((x+y)^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((a+b)^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((5 x-y)^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((a-3 b)^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((3 s+2 t)^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((3 p-4 q)^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((u+v)^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((b-c)^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((2 x-3 y)^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, use the distributive property to expand the binomial. \((4 m+3 n)^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, expand the binomial using a calculator to find the binomial coefficients. \((a+b)^{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, expand the binomial using a calculator to find the binomial coefficients. \((a+b)^{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, expand the binomial using a calculator to find the binomial coefficients. \((x+y)^{7}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, expand the binomial using a calculator to find the binomial coefficients. \((x+y)^{10}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, expand the binomial using Pascals triangle to find the coefficients. \((x+y)^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, expand the binomial using Pascals triangle to find the coefficients. \((x+y)^{5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, expand the binomial using Pascals triangle to find the coefficients. \((p+q)^{8}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, expand the binomial using Pascals triangle to find the coefficients. \((p+q)^{9}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, evaluate the expression by hand (using the formula) before checking your answer on a grapher. \(\left(\begin{array}{l} 9 \\ 2 \end{array}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, evaluate the expression by hand (using the formula) before checking your answer on a grapher. \(\left(\begin{array}{l} 15 \\ 11 \end{array}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, evaluate the expression by hand (using the formula) before checking your answer on a grapher. \(\left(\begin{array}{l} 166 \\ 166 \end{array}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, evaluate the expression by hand (using the formula) before checking your answer on a grapher. \(\left(\begin{array}{c} 166 \\ 0 \end{array}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, find the coefficient of the given term in the binomial expansion. \(x^{11} y^{3}\) term, \((x+y) 14\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, find the coefficient of the given term in the binomial expansion. \(x^{5} y^{8}\) term, \((x+y)^{13}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, find the coefficient of the given term in the binomial expansion. \(x^{4}\) term, \((x-2)^{12}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, find the coefficient of the given term in the binomial expansion. \(x^{7}\) term, \((x-3)^{11}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, use the Binomial Theorem to find a polynomial expansion for the function. \(f(x)=(x-2)^{5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, use the Binomial Theorem to find a polynomial expansion for the function. \(g(x)=(x+3)^{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, use the Binomial Theorem to find a polynomial expansion for the function. \(h(x)=(2 x-1)^{7}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, use the Binomial Theorem to find a polynomial expansion for the function. \(f(x)=(3 x+4)^{5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2126, use the Binomial Theorem to expand each expression. \((2 x+y)^{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2126, use the Binomial Theorem to expand each expression. \((2 y-3 x)^{5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2126, use the Binomial Theorem to expand each expression. \((\sqrt{x}-\sqrt{y})^{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2126, use the Binomial Theorem to expand each expression. \((\sqrt{x}+\sqrt{3})^{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2126, use the Binomial Theorem to expand each expression. \(\left(x^{-2}+3\right)^{5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2126, use the Binomial Theorem to expand each expression. \(\left(a-b^{-3}\right)^{7}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Determine the largest integer n for which your calculator will compute n!.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Determine the largest integer n for which your calculator will compute \(\left(\begin{array}{c} n \\ 100 \end{array}\right)\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that \(\left(\begin{array}{l} n \\ 1 \end{array}\right)=\left(\begin{array}{c} n \\ n-1 \end{array}\right)=n\) for all integers \(n \geq 1\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that \(\left(\begin{array}{l} n \\ r \end{array}\right)=\left(\begin{array}{c} n \\ n-r \end{array}\right)\) for all integers \(n \geq r \geq 0\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use the formula \(\left(\begin{array}{l} n \\ r \end{array}\right)=\frac{n !}{r !(n-r) !}\) to prove that \(\left(\begin{array}{l} n \\ r \end{array}\right)=\left(\begin{array}{l} n-1 \\ r-1 \end{array}\right)+\left(\begin{array}{c} n-1 \\ r \end{array}\right)\). (This is the pattern in Pascals trian

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Find a counterexample to show that each statement is false. (a) (n + m)! = n! + m! (b) (nm)! = n!m!

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that \(\left(\begin{array}{l} n \\ 2 \end{array}\right)+\left(\begin{array}{c} n+1 \\ 2 \end{array}\right)=n^{2}\) for all integers \(n \geq 2\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that \(\left(\begin{array}{c} n \\ n-2 \end{array}\right)+\left(\begin{array}{l} n+1 \\ n-1 \end{array}\right)=n^{2}\) for all integers \(n \geq 2\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The coefficients in the polynomial expansion of \((x-y)^{50}\) alternate in sign. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The sum of any row of Pascals triangle is an even integer. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
What is the coefficient of \(x^{4}\) in the expansion of \((2 x+1)^{8}\)? (A) 16 (B) 256 (C) 1120 (D) 1680 (E) 26,680

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following numbers does not appear on row 10 of Pascals triangle? (A) 1 (B) 5 (C) 10 (D) 120 (E) 252

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The sum of the coefficients of \((3x - 2y)^{10}\) is (A) 1. (B) 1024. (C) 58,025. (D) 59,049. (E) 9,765,625.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
\((x + y)^{3} + (x - y)^{3} = \) (A) 0. (B) \(2x^{3}\). (C) \(2x^{3} - 2y^{3}\). (D) \(2x^{3} + 6xy^{2}\). (E) \(6x^{2} y + 2y^{3}\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Numbers of the form \(1+2+\cdots+n\) are called triangular numbers because they count numbers in triangular arrays, as shown below: (a) Compute the first 10 triangular numbers. (b) Where do the triangular numbers appear in Pascals triangle? (c) Explain why the diagram below shows

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exploring Pascals Triangle Break into groups of two or three. Just by looking at patterns in Pascals triangle, guess the answers to the following questions. (It is easier to make a conjecture from a pattern than it is to construct a proof!) (a) What positive integer appears the least number o

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use the Binomial Theorem to prove that the sum of the entries along the nth row of Pascals triangle is \(2^{n}\). That is, \(\left(\begin{array}{l} n \\ 0 \end{array}\right)+\left(\begin{array}{l} n \\ 1 \end{array}\right)+\left(\begin{array}{l} n \\ 2 \end{array}\right)+\cdots+\left(\begin{array

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use the Binomial Theorem to prove that the alternating sum along any row of Pascals triangle is zero. That is, \(\left(\begin{array}{l} n \\ 0 \end{array}\right)-\left(\begin{array}{l} n \\ 1 \end{array}\right)+\left(\begin{array}{l} n \\ 2 \end{array}\right)-\cdots+(-1)^{n}\left(\begin{array}{l}

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use the Binomial Theorem to prove that \(\left(\begin{array}{l} n \\ 0 \end{array}\right)+2\left(\begin{array}{l} n \\ 1 \end{array}\right)+4\left(\begin{array}{l} n \\ 2 \end{array}\right)+\cdots+2^{n}\left(\begin{array}{l} n \\ n \end{array}\right)=3^{n}\).