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: 34

Answer

$a^7 - 7 a^6 b + 21 a^5 b^2 - 35 a^4 b^3 + 35 a^3 b^4 - 21 a^2 b^5 + 7 a b^6 - b^7$

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: $n=7$, $(a-b)^7=\binom{7}{0}a^7(-b)^0+\binom{7}{1}a^{7-1}(-b)^1+\binom{7}{2}a^{7-2}(-b)^2+\binom{7}{3}a^{7-3}(-b)^3+\binom{7}{4}a^{7-4}(-b)^4+\binom{7}{5}a^{7-5}(-b)^5+\binom{7}{6}a^{7-6}(-b)^6+\binom{7}{7}a^{7-7}(-b)^7$ $a^7 - 7 a^6 b + 21 a^5 b^2 - 35 a^4 b^3 + 35 a^3 b^4 - 21 a^2 b^5 + 7 a b^6 - b^7$
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