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: 23

Answer

$x^{10}+5x^8y^2+10x^6y^4+10x^4y^6+5x^2y^8+y^{10}$

Work Step by Step

We are given the expression: $(x^2+y^2)^5$ Use the Binomial Theorem to expand the expression: $(x^2+y^2)^5=\sum_{k=0}^5 \binom{5}{k}(x^2)^{5-k}(y^2)^k$ $=\binom{5}{0}(x^2)^5(y^2)^0+\binom{5}{1}(x^2)^4(y^2)^1+\binom{5}{2}(x^2)^3(y^2)^2+\binom{5}{3}(x^2)^2(y^2)^3+\binom{5}{4}(x^2)^1(y^2)^4+\binom{5}{5}(x^2)^0(y^2)^5$ $=x^{10}+5x^8y^2+10x^6y^4+10x^4y^6+5x^2y^8+y^{10}$
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