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

 Question 

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

Solution

Verified by GMS

(x−y−x)(x2+y2+z2+xy−yz+xz)

According to the equation,
a3−b3−c3−3abc=(a−b−c)(a2+b2+c2+ab−bc+ca)

The given question can be written as 
=(x3+xy2+x2y−xyz+x2z−x2y−y3−yz2−xy2+y2z−xyz−x2z−y2z−z3−xyz+yz2−xz2)

So we get,

=(x3−y3−z3−xyz−xyz−xyz)
=x3−y3−z3−3xyz