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

(N/A) To verify the identity,we start with the Right Hand Side ($R$.$H$.$S$.):
$R.H.S. = (x-y)(x^{2}+xy+y^{2})$
Distribute the terms:
$= x(x^{2}+xy+y^{2}) - y(x^{2}+xy+y^{2})$
$= (x^{3} + x^{2}y + xy^{2}) - (x^{2}y + xy^{2} + y^{3})$
$= x^{3} + x^{2}y + xy^{2} - x^{2}y - xy^{2} - y^{3}$
Cancel the like terms with opposite signs ($x^{2}y - x^{2}y = 0$ and $xy^{2} - xy^{2} = 0$):
$= x^{3} - y^{3}$
$= L.H.S.$
Since $L.H.S. = R.H.S.$,the identity is verified.