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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. 223 (page 1213)

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

Short Answer

Expert verified

The binomial expansion is $625 x^{4} - 1000 x^{3} y + 600 x^{2} y^{2} - 160 x y^{3} + 16 y^{4}$ .

Step by step solution

01

Step 1. Given Information.

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

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:-

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

Simplify the expression:-

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

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Most popular questions from this chapter

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