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: 18



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 $(x^2+y)^4=\displaystyle \binom{4}{0}(x^2)^4(y)^0+\displaystyle \binom{4}{1}(x^2)^3(y)^1+\displaystyle \binom{4}{2}(x^2)^2(y)^2+\displaystyle \binom{4}{3}(x^2)^1(y)^3+\displaystyle \binom{4}{4}(x^2)^0(y)^4$ $=x^8(1)+(4)(x^6)(y)+(6)(x^4)(y^2)+4(x^2)(y^3)+(y^4)(1)$ $\bf{(Simplify)}$ $=x^8+4x^6y+6x^4y^2+4x^2y^3+y^4$
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