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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. 224 (page 1213)

In the following exercises, expand each binomial ${(2 x 鈥� + 鈥� 5 y)}^{4}$ .

Short Answer

Expert verified

The solution of the exercise is $16 x^{4} + 160 x^{3} y + 600 x^{2} y^{2} + 1000 x y^{3} + 625 y^{4}$ .

Step by step solution

01

Step 1. Given Information.

Given Binomial expression is ${(2 x 鈥� + 鈥� 5 y)}^{4}$ .

02

Step 2. Binomial expansion formula .

The binomial expansion formula is :-

${(a + b)}^{n} = {鈭�}_{i = 0}^{n} (\binom{n}{i}) a^{(n - i)} b^{i}$

03

Step 3. Solve Binomial Expansion

Expanding using Binomial theorem:-

${(2 x 鈥� + 鈥� 5 y)}^{4} = {鈭�}_{i = 0}^{4} (\binom{4}{i}) {(2 x)}^{(4 - i)} {(5 y)}^{i} {鈭�}_{i = 0}^{4} (\binom{4}{i}) {(2 x)}^{(4 - i)} {(5 y)}^{i} = \frac{4!}{0! (4 - 0)!} {(2 x)}^{4} {(5 y)}^{0} + \frac{4!}{1! (4 - 1)!} {(2 x)}^{3} {(5 y)}^{1} + \frac{4!}{2! (4 - 2)!} {(2 x)}^{2} {(5 y)}^{2} + \frac{4!}{3! (4 - 3)!} {(2 x)}^{1} {(5 y)}^{3} + \frac{4!}{4! (4 - 4)!} {(2 x)}^{0} {(5 y)}^{4}$

Simplify the expression:-

$16 x^{4} + 160 x^{3} y + 600 x^{2} y^{2} + 1000 x y^{3} + 625 y^{4}$ .

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