Let (x + y) = a and (x - y) = b
Then, (x + y)3 + (x - y)3 + 6x(x2 - y2) = (x + y)3 + (x - y)3 + 3 x 2\(x\) x (x + y)(x - y)
= (x + y)3 + (x - y)3 - 3 x [(x + y) + (x - y)] x (x + y) + (x - y)
= a3 + b3 + 3ab(a + b)
= (a + b)3 = (x + y + x - y)3 = (2x)3 = 8x3.
