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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 316 (page 1221)

In the following exercises, find the indicated term in the expansion of the binomial : Third term of ${(x - y)}^{7}$ .

Short Answer

Expert verified

The third term of the given binomial ${(x - y)}^{7}$ is $21 x^{5} y^{2}$ .

Step by step solution

01

Step 1. Given

A binomial is given as ${(x - y)}^{7}$ .

To find the third term of the given binomial.

02

Step 2. Use the formula of binomial expansion (a+b)n=C0nan-0b0+C1nan-1b+…+Cnnan-nbn.

Substitute $n = 7 r = 2$ in the formula ${}^{n}C_{r} x^{n - r} y^{r}$ which gives

${}^{7}C_{2} x^{7 - 2} y^{2} = {}^{7}C_{2} x^{5} y^{2} = \frac{7! 鈥�}{(7 - 2)! 鈥� 2! 鈥�} x^{5} y^{2} = \frac{7! 鈥�}{5! 鈥� 2! 鈥�} x^{5} y^{2} = 21 x^{5} y^{2}$

The third term of the given binomial is $21 x^{5} y^{2}$ .

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