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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. 221 (page 1213)

In the following exercises, expand each binomial ${(q 鈥� 鈭� 鈥� 4)}^{3}$ .

Short Answer

Expert verified

The Binomial expansion is $q^{3} - 12 q^{2} + 48 q - 64$ .

Step by step solution

01

Step 1. Given Information.

Given Binomial expression is ${(q 鈥� 鈭� 鈥� 4)}^{3}$ .

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:-

${(q 鈥� 鈭� 鈥� 4)}^{3} = {鈭�}_{i = 0}^{3} (\binom{3}{i}) p^{(3 - i)} {(- 4)}^{i}$

${(q 鈥� 鈭� 鈥� 4)}^{3} = {鈭�}_{i = 0}^{3} (\binom{3}{i}) p^{(3 - i)} {(- 4)}^{i} = q^{3} - 12 q^{2} + 48 q - 64$

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Most popular questions from this chapter

In the following exercises, evaluate.

(a) $(\begin{array}{l} 4 \\ 1 \end{array})$ (b) $(\begin{array}{l} 5 \\ 5 \end{array})$ (c) $(\begin{array}{l} 8 \\ 0 \end{array})$ (d) $(\begin{array}{l} 11 \\ 9 \end{array})$

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