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: 17

Answer

$x^5+5x^4+10x^2+5x+1$

Work Step by Step

We are given the expression: $(x+1)^5$ Use the Binomial Theorem to expand the expression: $(x+1)^5=\sum_{k=0}^5 \binom{5}{k}x^{5-k}1^k$ $=\binom{5}{0}x^5+\binom{5}{1}x^4+\binom{5}{2}x^3+\binom{5}{3}x^2+\binom{5}{4}x^1+\binom{5}{5}$ $=x^5+5x^4+10x^2+5x+1$
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