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: 48



Work Step by Step

Calculate the terms containing $y^{6}$ for $(x+2y)^{10}$ 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,$(x+2y)^{10}=\displaystyle \binom{10}{6}x^{(10-6)}(2y)^{6}$ or,$=(2)^6[\dfrac{10!}{6!(10-6)!}]x^{4}(y)^{6}$ $=[\dfrac{10 \times 9 \times 8 \times 7 \times 6!}{6!(4 \times 3 \times 2 \times 1)}](x)^{16}y^{14}$ Hence, Terms containing for $y^{6}$ are: $13440x^{4}y^{6}$
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