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: 19



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 $(y-3)^4=\displaystyle \binom{4}{0}(y)^4(-3)^0+\displaystyle \binom{4}{1}(y)^3(-3)^1+\displaystyle \binom{4}{2}(y)^2(-3)^2+\displaystyle \binom{4}{3}(y)^1(-3)^3+\displaystyle \binom{4}{4}(y)^0(-3)^4$ $=y^4(1)+(4)(y^3)(-3)+(6)(y^2)(9)+(4)(y)(-27)+(81)(1)$ $\bf{(Simplify)}$ $=y^4-12y^3+54y^2-108y+81$
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