Question

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

Answer 1

Answer:

2y^3+2x^2y

Step-by-step explanation:

1) (x^2+y^2+2xy)(x+y)

=x^3+xy^2+2x^2y+x^2y+y^3+2xy^2

=x^3+3xy^2+3x^2y+y^3

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

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

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

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

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

=2y^3+2x^2y