Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - 11.4 The Binomial Theorem - 11.4 Exercises: 33

Answer

$p^5 - 5 p^4 q + 10 p^3 q^2 - 10 p^2 q^3 + 5 p q^4 - q^5$

Work Step by Step

$(x+y)^n=\binom{n}{0}x^ny^0+\binom{n}{1}x^{n-1}y^1+...+\binom{n}{a}x^{n-a}y^a+..\binom{n}{n}x^{0}y^n$ Here: $n=5$, $(p-q)^5=\binom{5}{0}p^5(-q)^0+\binom{5}{1}p^{5-1}(-q)^1+\binom{5}{2}p^{5-2}(-q)^2+\binom{5}{3}p^{5-3}(-q)^3+\binom{5}{4}p^{5-4}(-q)^1+\binom{5}{5}p^{5-5}(-q)^5=$ $p^5 - 5 p^4 q + 10 p^3 q^2 - 10 p^2 q^3 + 5 p q^4 - q^5$
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