Chapter 6: Q. 227 (page 604)

In the following exercises, factor completely.
${(x + 1)}^{3} + 8 x^{3}$

Short Answer

Expert verified

The simplified expression is $(3 x + 1) (3 x^{2} + 1)$

Step by step solution

Step 1. Given Information

The given expression is ${(x + 1)}^{3} + 8 x^{3}$

Step 2. Calculation

We will find the factor of binomial sum by using addition of cube pattern,

${(x + 1)}^{3} + 8 x^{3} = {(x + 1)}^{3} + {(2 x)}^{3} = ((x + 1) + 2 x) ({(x + 1)}^{2} - (x + 1) 2 x + {(2 x)}^{2}) = (x + 1 + 2 x) ({(x + 1)}^{2} - (2 x^{2} + 2 x) + 4 x^{2}) = (x + 1 + 2 x) ((x^{2} + 2 x + 1) - (2 x^{2} + 2 x) + 4 x^{2}) = (3 x + 1) (5 x^{2} - 2 x^{2} + 2 x - 2 x + 1) = (3 x + 1) (3 x^{2} + 1)$

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In the following exercises, factor completely.
${(x + 1)}^{3} + 8 x^{3}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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In the following exercises, factor completely.(x+1)3+8x3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Mechanics Maths

Logic and Functions

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely.
${(x + 1)}^{3} + 8 x^{3}$