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Chapter 6: Q. 6.62 (page 599)

Factor:y3+8.

Short Answer

Expert verified

Factors ofy3+8arey+2y2-2y+4.

Step by step solution

01

Step 1. Given information. 

Given an expression y3+8.

02

Step 2. Check if it is a sum or difference of cubes pattern.

It can be seen that y3+8=y3+23.

The expression is sum of cubes pattern.

03

Step 3. Use either the sum or difference of cubes pattern and simplify.

Note that a3+b3=a+ba2-ab+b2..

The expression is sum of cubes.

y3+8=y3+23=y+2y2-2y+4

So, y3+8=y+2y2-2y+4.

04

Step 4. Check by multiplying the factors.

Verify as follows.

y+2y2-2y+4=yy2-2y+4+2y2-2y+4=y3-2y2+4y+2y2-4y+8=y3+8

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