Verify: $x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})$

(N/A) To verify the identity,we expand the right-hand side ($R$.$H$.$S$.).
$R.H.S. = (x+y)(x^{2}-xy+y^{2})$
$= x(x^{2}-xy+y^{2}) + y(x^{2}-xy+y^{2})$
$= (x^{3} - x^{2}y + xy^{2}) + (x^{2}y - xy^{2} + y^{3})$
By grouping the like terms,we get:
$= x^{3} + (-x^{2}y + x^{2}y) + (xy^{2} - xy^{2}) + y^{3}$
$= x^{3} + 0 + 0 + y^{3}$
$= x^{3} + y^{3} = L.H.S.$
Hence,the identity is verified.