Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.4 The Binomial Theorem - 14.4 Exercise Set: 47

Answer

$1120x^{12}y^2$

Work Step by Step

The $r+1$ th term in the binomial expansion of $(x+y)^n$ is: $\binom{n}{r}x^{n-r}y^r$ Here $x=2x^3$, $y=\sqrt{y}$, $n=8$: $r+1=5$ $r=4$ The indicated term is: $\binom{8}{4}(2x^3)^{8-4}(\sqrt{y})^4=70\times2^4\times x^{12}\times y^2=1120x^{12}y^2$
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