Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.5 - The Binomial Theorum - Exercise Set - Page 1092: 42



Work Step by Step

Calculate the fifth term for $(x-1)^{10}$ by using General formula such as:$(m+n)^r=\displaystyle \binom{r}{k}m^{r-k}n^k$ and $\displaystyle \binom{r}{k}=\dfrac{r!}{k!(r-k)!}$ This implies, $(x-1)^{10}=\displaystyle \binom{10}{4}x^{({10-4})}(-1)^4$ or,$=\dfrac{10!}{4!(10-4)!}(x)^{6}(-1)^4$ or, $=\dfrac{ 10 \times 9 \times 8 \times 7 \times 6!}{4 \times 3 \times 2 \times 1(6!)}x^{6}$ or, $=210x^6$
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