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: 40



Work Step by Step

Calculate the third term for $(x+2y)^{6}$ 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, $(x+2y)^{6}=\displaystyle \binom{6}{2}(2x)^{6-2}(2y)^2$ or,$=\dfrac{6!}{2!(6-2)!}(x)^{4}(2)^2y^2$ or, $=(4)\dfrac{6 \times 5 \times 4!}{2 \times 1(4!)}(x)^{4}(y)^2$ or, $=60x^4y^2$
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