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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. 225 (page 1213)

In the following exercises, expand each binomial ${(3 x 鈥� + 鈥� 4 y)}^{5}$ .

Short Answer

Expert verified

The solution of the exercise is

$243 x^{5} + 1620 x^{4} y + 4320 x^{3} y^{2} + 5760 x^{2} y^{3} + 3840 x y^{4} + 1024 y^{5}$

Step by step solution

01

Step 1. Given Information.

Given Binomial expression is ${(3 x 鈥� + 鈥� 4 y)}^{5}$ .

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:-

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

Simplify the expression:-

$243 x^{5} + 1620 x^{4} y + 4320 x^{3} y^{2} + 5760 x^{2} y^{3} + 3840 x y^{4} + 1024 y^{5}$

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Most popular questions from this chapter

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