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 - Page 676: 37


The 3rd term is $\binom{9}{2}3^7(-2)^2x^7=36\times 2187\times 4x^7=314928x^7$

Work Step by Step

By using the binomial theorem we can expand the algebraic expression in the form of: $(ax+b)^n=\binom{n}{0}a^nb^0x^n+\binom{n}{1}a^{n-1}b^1x^{n-1}+...+\binom{n}{n-i}a^{i}b^{n-i}x^{i}+...+\binom{n}{n-1}a^1b^{n-1}x^1+\binom{n}{n}a^0b^nx^0$ We expand the given expression: $(3x-2)^9=\binom{9}{0}3^9(-2)^0x^9+\binom{9}{1}3^8(-2)^1x^8+\binom{9}{2}3^7(-2)^2x^7+\binom{9}{3}3^6(-2)^3x^6+\binom{9}{4}3^5(-2)^4x^5+\binom{9}{5}3^4(-2)^5x^4+\binom{9}{6}3^3(-2)^6x^3+\binom{9}{7}3^2(-2)^7x^2+\binom{9}{8}3^1(-2)^8x^1+\binom{9}{9}3^0(-2)^9x^0$ The 3rd term is $\binom{9}{2}3^7(-2)^2x^7=36\times 2187\times 4x^7=314928x^7$
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