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: 42

Answer

$210x^6$

Work Step by Step

Our aim is to find the fifth term for $(x-1)^{10}$. General formula:$(p+q)^n=\displaystyle \binom{n}{k}p^{n-k}q^k$ and $\displaystyle \binom{n}{k}=\dfrac{n!}{k!(n-k)!}$ Now, $(x-1)^{10}=\displaystyle \binom{10}{4}(x)^{10-4}(-1)^4$ This implies, $=\dfrac{10!}{4!(10-4)!}(x)^{6}(-1)^4$ $=\dfrac{ 10 \times 9 \times 8 \times 7 \times 6!}{4 \times 3 \times 2 \times 1(6!)}(x)^{6}$ Thus, $=210x^6$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.