Chapter 12: Q. 221 (page 1213)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given Information.

Given Binomial expression is ${(q - 4)}^{3}$ .

Step 2. Binomial expansion formula .

The binomial expansion formula is :-

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

Step 3. Solve Binomial Expansion

Expanding using Binomial Theorem:-

${(q - 4)}^{3} = \sum_{i = 0}^{3} (\binom{3}{i}) p^{(3 - i)} {(- 4)}^{i}$

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

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

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Binomial expansion formula .

Step 3. Solve Binomial Expansion

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Step by step solution

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Step 3. Solve Binomial Expansion

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