Please help!

(X+y)^3+(x-y)^3

2 answers

a^3-b^3 = (a-b)(a^2+ab+b^2)

So, using a=x+y and b=x-y

(x+y)^3 - (x-y)^3
= ((x+y)-(x-y))((x+y)^2+(x+y)(x-y)+(x-y)^2)
= (2y)(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)
= (2y)(3x^2+y^2)

Thanks so much steve!