Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 11 - Section 11.4 - The Binomial Theorem - Exercise Set - Page 865: 39



Work Step by Step

Our aim is to find the third term for $(2x+y)^{6}$. General formula:$(p+q)^n=\displaystyle \binom{n}{k}p^{n-k}q^k$ and $\displaystyle \binom{n}{k}=\dfrac{n!}{k!(n-k)!}; k=2$ Now, $(2x+y)^{6}=\displaystyle \binom{6}{2}(2x)^{6-2}(y)^2$ This implies, $=\dfrac{6!}{2!(6-2)!}(2x)^{4}(y)^2$ $=\dfrac{6 \times 5 \times 4!}{2 \times 1(4!)}(2x)^{4}(y)^2$ Thus, $=240x^4y^2$
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