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: 27



Work Step by Step

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