Question

Find The Product : (x−y−x)(x 2 +y 2 +z 2 +xy−yz+xz)

## Solution

Verified by GMS

Question

Find The Product : (x−y−x)(x 2 +y 2 +z 2 +xy−yz+xz)

Verified by GMS

According to the equation,

$a_{3}−b_{3}−c_{3}−3abc=(a−b−c)(a_{2}+b_{2}+c_{2}+ab−bc+ca)$

The given question can be written as

$=(x_{3}+xy_{2}+x_{2}y−xyz+x_{2}z−x_{2}y−y_{3}−yz_{2}−xy_{2}+y_{2}z−xyz−x_{2}z−y_{2}z−z_{3}−xyz+yz_{2}−xz_{2})$

So we get,

$=(x_{3}−y_{3}−z_{3}−xyz−xyz−xyz)$

$=x_{3}−y_{3}−z_{3}−3xyz$

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