Question

Factorise: (x-y)³-8(x+y)³ with full steps​

Answer 1

a3−b3=(a−b)(a2+ab+b2)

Also, we know that 8=23

and a3b3=(ab)3

So (x−y)3−8(x+y)3

= (x−y)3−(2x+2y)3

=[(x−y)−(2x+2y)][(x−y)2+(x−y)(2x+2y)+(2x+2y)2]

=  (−x−3y)

7x^{2} + 6xy + 3y^{2}

So

=  (−x-3y)[7x^2+6xy+3y^2]