Answer
$[(x-1)+1]^{5}=x^{5}$
Work Step by Step
We need to factor:
$(x-1)^{5}+5(x-1)^{4}+10(x-1)^{3}+10(x-1)^{2}+5(x-1)+1$
We notice that this corresponds to an expanded binomial with a power of $5$ and terms $x-1$ and $1$:
$[(x-1)+1]^{5}=x^{5}$
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
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 - Page 636: 44
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