Verify:

(i) $x^3+y^3=(x+y)(x^2-xy+y^2)$
(ii) $x^3-y^3=(x-y)(x^2+xy+y^2)$

To verify put $x=1$ and $y=2$ in given equations, and check wheater LHS and RHS are equal.

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

LHS: $x^3+y^3=$ $1^3+2^3$ $=9$

RHS: $=(x+y)(x^2-xy+y^2)$ $=(1+2)(1^2-1.2+2^2)$ $=9$

verified

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

LHS:$x^3-y^3=$ $1^3-2^3$ $=-7$

RHS:$(x-y)(x^2+xy+y^2)$$=(1-2)(1^2+1.2+2^2)$ $=-7$

It is verified