Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Section 11.5 - The Binomial Theorem - Exercise Set - Page 664: 25

Answer

$625 a^4 - 1000 a^3 b + 600 a^2 b^2 - 160 a b^3 + 16 b^4$

Work Step by Step

Using the Binomial Formula, the expression $ (5a-2b)^4 $ expands to \begin{array}{l} (5a)^4(-2b)^0+ \dfrac{4}{1!}(5a)^3(-2b)^1+ \dfrac{4\cdot4}{2!}(5a)^2(-2b)^2+\\ \dfrac{4\cdot4\cdot3\cdot2}{3!}(5a)^1(-2b)^3+ \dfrac{4\cdot4\cdot3\cdot2\cdot1}{4!}(5a)^0(-2b)^4 \\\\= 625 a^4 - 1000 a^3 b + 600 a^2 b^2 - 160 a b^3 + 16 b^4 \end{array}
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