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Chapter 7: Q 258 (page 867)

In the following exercises, the factor:

6x3-48y3

Short Answer

Expert verified

The factorization of the expression is 6(x-2y)(x2+2xy+4y2)

Step by step solution

01

Step 1. Given information

Given expression is6x3-48y3

02

Step  2.  Find the Greatest Common Factor and write the terms as the cube.

The G.C.F is 6

a3-b3=6x3-(2y)3

03

Step 3.  Write the difference in the cubes pattern and simplify.

(a-b)(a2+ab+b2)=6(x-2y)x2+2脳x脳y+(2y)2=6(x-2y)(x2+2xy+4y2)

04

Step 4. Check

6(x-2y)(x2+2xy+4y2)=6(x3-2x2y+2x2y-4xy2+4xy2-8y3)=6(x3-8y3)=6x3-48y3

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