Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 11 - Section 11.4 - The Binomial Theorem - Exercise Set - Page 865: 41



Work Step by Step

Our aim is to find the fifth term for $(x-1)^{9}$. General formula:$(p+q)^n=\displaystyle \binom{n}{k}p^{n-k}q^k$ and $\displaystyle \binom{n}{k}=\dfrac{n!}{k!(n-k)!}; k=2$ Now, $(x-1)^{9}=\displaystyle \binom{9}{4}(x)^{9-4}(-1)^4$ This implies, $=\dfrac{9!}{4!(9-4)!}(x)^{5}(-1)^4$ $=\dfrac{9 \times 8 \times 6 \times 5!}{4 \times 3 \times 2 \times 1(5!)}(x)^{5}$ Thus, $=126x^5$
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