Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 11 - Section 11.4 - The Binomial Theorem - Exercise Set - Page 864: 15

Answer

$16x^4+32x^3+24x^2+8x+1$

Work Step by Step

According to the Binomial Theorem or Binomial expansion, the expansion for $(x+y)$ in the any number of power can be calculated as: $(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$ Let's see how this formula works: $(2x+1)^4=\displaystyle \binom{4}{0}(2x)^4(1)^0+\displaystyle \binom{4}{1}(2x)^3(1)^1+\displaystyle \binom{4}{2}(2x)^2(1)^2+\displaystyle \binom{4}{3}(2x)^1(1)^3+\displaystyle \binom{4}{4}(2x)^0(1)^3$ or, $=16x^4+4(8x^3)(1)+24x^2+8x+1$ or, $=16x^4+32x^3+24x^2+8x+1$
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