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 - Page 922: 50


$30x^{3/2}$ and $30\sqrt3x$

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 $x=\sqrt{x}$, $y=\sqrt{3}$, $n=5$: There are 6 terms in this expansion, the middle two are the 3 rd and 4th. 3rd term: $r+1=3$ $r=2$ $\binom{5}{2}(\sqrt{x})^{5-2}(\sqrt{3})^2=10x^{3/2}\times 3=30x^{3/2}$ 4th term: $r+1=4$ $r=3$ $\binom{5}{3}(\sqrt{x})^{5-3}(\sqrt{3})^3=10x\times 3\sqrt3=30\sqrt3x$
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