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: 31



Work Step by Step

According to Binomial Theorem, the term containing $x^k$ in the expansion of $(x+p)^n$ can be determined as: $\displaystyle{n}\choose{n-k}$$ p^{n-k}x^k (1)$ Using formula (1), replacing $x$ with $2x$ and $c$ with $-1$, the term containing $x^7$ in the expansion of $(2x-1)^{12}$ can be written as: $\displaystyle{12}\choose{12-7}$ $(-1)^{12-7}(2x)^7 =$$\\\displaystyle{12}\choose{5}$ $(-1)^{5}(2x)^7 \\=\displaystyle\dfrac{12!}{5!7!} (-1)(128x^7) \\=(792) (-128x^7) \\=-101,376x^7$ Therefore, the coefficient of the term that contains $x^7$ is: $-101,376$
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