Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 37


The 3rd term is $314928 \ x^7$

Work Step by Step

According to the binomial theorem, we can expand the algebraic expression in the form of: $(a+b)^n=\binom{n}{0}b^0a^n+\binom{n}{1} b^1a^{n-1}++\binom{n}{n-i} b^{n-i}a^{i}++\binom{n}{n-1}b^{n-1}a^1+\binom{n}{n}b^nx^0$ Now, we will expand the given expression by replacing $(a+b)^n$ with $(3x-2)^9$. $(3x-2)^9=\binom{9}{0}(3x)^9(-2)^0+\binom{9}{1}(-2)^1(3x)^8+\binom{9}{2}3^7(-2)^2x^7+\binom{9}{3}(-2)^3(3x)^6+\binom{9}{4}(-2)^4 (3x)^5+\binom{9}{5}(-2)^5(3x)^4+\binom{9}{6}(-2)^6(3x)^3+\binom{9}{7}(-2)^7(3x)^2+\binom{9}{8}(-2)^8(3x)^1+\binom{9}{9}(-2)^9(3x)^0$ So, the 3rd term is $\dbinom{9}{2}(-2)^2(3x)^7=36\times 2187\times 4 \times x^7=314928 \ x^7$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.