Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 34

Answer

The coefficient of the term that contains $x^2$ is equal to $-314928$.

Work Step by Step

According to the Binomial Theorem, the term containing $x^k$ in the expansion of $(p+q)^n$ can be determined as: $\displaystyle{n}\choose{n-k}$$ p^{n-k} q^k$ Using the above formula and replacing $p$ with $2$ and $q$ with $-3$, the term containing $x^2$ in the given expansion can be written as: $\dbinom{9}{9-2} \ (2)^{2}(-3)^{9-2} =\dbinom {9} {7} (2)^{2}(-3)^7 \\= \dfrac{9!}{7! \ 2!} (2)^{2}(-3)^7 \\=36 \times 4 \times (-2187) \\=-314928$ Therefore, the coefficient of the term that contains $x^2$ is equal to $-314928$
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