College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.5 - The Binomial Theorem - 9.5 Assess Your Understanding: 33



Work Step by Step

By using the binomial theorem we can expand the algebraic expression in the form of: $(ax+b)^n=\binom{n}{0}a^nb^0x^n+\binom{n}{1}a^{n-1}b^1x^{n-1}+...+\binom{n}{n-i}a^{i}b^{n-i}x^{i}+...+\binom{n}{n-1}a^1b^{n-1}x^1+\binom{n}{n}a^0b^nx^0$ There, we can see that the coefficient of $x^i$ is $\binom{n}{n-i}a^{i}b^{n-i}$. In this case, $a=2$, $b=3$, $n=9$, $i=7$; therefore, the coefficient will be: $\binom{9}{9-7}2^73^{9-7}=\binom{9}{2}2^73^2=36\times 128\times 9=41,472$
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