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: 49

Answer

$7,838,208\sqrt2u^{5}$

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 $x=2u$, $y=3\sqrt{2}$, $n=10$: There are 11 terms in this expansion, the middle one is the 6th. $r+1=6$ $r=5$ The indicated term is: $\binom{10}{5}(2u)^{10-5}(3\sqrt{2})^5=252\times2^5\times u^{5}\times 972\sqrt2=7,838,208\sqrt2u^{5}$
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