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Chapter 6: Q. 227 (page 604)

In the following exercises, factor completely.

(x+1)3+8x3

Short Answer

Expert verified

The simplified expression is 3x+13x2+1

Step by step solution

01

Step 1. Given Information  

The given expression is(x+1)3+8x3

02

Step 2. Calculation 

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

(x+1)3+8x3=(x+1)3+(2x)3=((x+1)+2x)((x+1)2-(x+1)2x+(2x)2)=(x+1+2x)((x+1)2-(2x2+2x)+4x2)=(x+1+2x)((x2+2x+1)-(2x2+2x)+4x2)=(3x+1)(5x2-2x2+2x-2x+1)=(3x+1)(3x2+1)

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