Q. 227 - Intermediate Algebra

Question

In the following exercises, factor completely. 

${(x+1)}^3+8x^3$

Step-by-Step Solution

Answer

The simplified expression is  $\left(3x+1\right)\left(3x^2+1\right)$

Step 1. Given Information

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

Step 2. Calculation

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

$$\begin{gathered} {(x+1)}^3+8x^3={(x+1)}^3+{\left(2x\right)}^3 \\ =\left(\right(x+1)+2x)({(x+1)}^2-(x+1)2x+{\left(2x\right)}^2) \\ =(x+1+2x)({(x+1)}^2-(2x^2+2x)+4x^2) \\ =(x+1+2x)\left(\right(x^2+2x+1)-(2x^2+2x)+4x^2) \\ =(3x+1)(5x^2-2x^2+2x-2x+1) \\ =(3x+1)(3x^2+1) \end{gathered}$$