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: 47



Work Step by Step

Calculate the terms containing $y^{14}$ for $(x^2+y)^{22}$ by using General formula such as:$(m+n)^r=\displaystyle \binom{r}{k}m^{r-k}n^k$ and $\displaystyle \binom{r}{k}=\dfrac{r!}{k!(r-k)!}$ This implies,$(x^2+y)^{32}=\displaystyle \binom{22}{14}(x^2)^{22-14}(y)^{14}$ or,$=\dfrac{22!}{14!(22-14)!}(x)^{16}y^{14}$ or,$=\dfrac{22!}{14!8!}x^{16}y^{14}$ or, $=319,770x^{16}y^{14}$ Hence, Terms containing for $y^{14}$ are: $319,770x^{16}y^{14}$
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