Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.5 The Binomial Theorem - 12.5 Assess Your Understanding - Page 836: 36



Work Step by Step

According to the Binomial Theorem, the nth term in the expansion of $(x+a)^k$ is given by: ${k\choose k-n+1}a^{n-1}x^{k-n+1}.$ Hence here for $n=3,k=7$: ${7\choose 7-3+1}(-3)^{3-1}x^{7-3+1}={7\choose 5}(-3)^{2}x^{5}=189x^5.$
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