Question

Factorise: x^8 - y^8

Answer 1

a*2-b*2=a+b(a-b)
So
a*8-b*8=a*4+b*4(a*4-b*4)
Now again by identity
(a*4+b*4)(a*2+b*2)(a*2-b*2)
(a*4+b*4)(a*2+b*2)(a+b)(a-b)

Answer 2

x^8 - y^8 = (x^4)^2 - (y^4)^2
               = (x^4 - y^4)(x^4 + y^4)
               = [(x^2)^2 - (y^2)^2] (x^4 + y^4)
               = (x^2 - y^2)( x^2+ y^2)(x^4 + y^4)
               = (x - y)(x+y)(x^2 + y^2)(x^4 + y^4)