Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.5 - The Binomial Theorum - Exercise Set - Page 1092: 20



Work Step by Step

Binomial Theorem or Binomial expansion can be defined as: $(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$ Need to apply the formula to get the Binomial Expansion. we have $(y-4)^4=\displaystyle \binom{4}{0}(y)^4(-4)^0+\displaystyle \binom{4}{1}(y)^3(-4)^1+\displaystyle \binom{4}{2}(y)^2(-4)^2+\displaystyle \binom{4}{3}(y)^1(-4)^3+\displaystyle \binom{4}{4}(y)^0(-4)^4$ $=(y^4)(1)+(4)(y^3)(-4)+(6)(y^2)(16)+(4)(y)(-64)+(256)(1)$$\bf{(Simplify)}$ $=y^4-16y^3+96y^2-256y+256$
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