College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.6 - The Binomial Theorem - 8.6 Exercises: 26

Answer

We expand using the Binomial Theorem: $(1-x)^{5}=1-5x+10x^{2}-10x^{3}+5x^{4}-x^{5}$

Work Step by Step

We expand using the Binomial Theorem: $(1-x)^{5}=\left(\begin{array}{l} 5\\ 0 \end{array}\right)(1)^{5}-\left(\begin{array}{l} 5\\ 1 \end{array}\right) (1)^{4}x^{1}+\left(\begin{array}{l} 5\\ 2 \end{array}\right)(1)^{3}x^{2}-\left(\begin{array}{l} 5\\ 3 \end{array}\right)(1)^{2}x^{3}+\left(\begin{array}{l} 5\\ 4 \end{array}\right)(1)^{1}x^{4}-\left(\begin{array}{l} 5\\ 5 \end{array}\right)x^{5}=1-5x+10x^{2}-10x^{3}+5x^{4}-x^{5}$
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