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 865: 31

Answer

$x^8+16x^7+112x^6$

Work Step by Step

Apply Binomial Theorem or Binomial expansion to find the first three terms of $(x+2)^8$. $(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$ Now, $(x+2)^8=\displaystyle \binom{8}{0}x^82^0+\displaystyle \binom{8}{1}8^72^1+\displaystyle \binom{8}{2}x^62^2$ $=(1)x^8(1)+8x^7(2)+28x^6(4)$ Thus, $(x+2)^8=x^8+16x^7+112x^6$
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