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: 35


The 5th term is equal to $2835 \ x^3$.

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 (x+3)^7. $(x+3)^7=\dbinom{7}{0}3^0x^7+\dbinom{7}{1}3^1x^6+\dbinom{7}{2}3^2x^5+\dbinom{7}{3}3^3x^4+\dbinom{7}{4}3^4x^3+\dbinom{7}{5}3^5x^2+\dbinom{7}{6}3^6x^1+\dbinom{7}{7}3^7x^0$ Thus, the 5th term is equal to $\dbinom{7}{4}3^4x^3=2835 \ x^3$
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