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: 28

Answer

$a^4x^4-4a^3bx^3y+6a^2b^2x^2y^2-4ab^3xy^3+b^4y^4$

Work Step by Step

We are given the expression: $(ax-by)^4$ Use the Binomial Theorem to expand the expression: $(ax-by)^4=\sum_{k=0}^4 \binom{4}{k}(ax)^{4-k}(-by)^k$ $=\binom{4}{0}(ax)^4(-by)^0+\binom{4}{1}(ax)^3(-by)^1+\binom{4}{2}(ax)^2(-by)^2+\binom{4}{3}(ax)^1(-by)^3+\binom{4}{4}(ax)^0(-by)^4$ $=a^4x^4+4a^3x^3(-by)+6a^2x^2(b^2y^2)+4ax(-b^3y^3)+b^4y^4$ $=a^4x^4-4a^3bx^3y+6a^2b^2x^2y^2-4ab^3xy^3+b^4y^4$
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