Question:
Find the value
$x\left(x^{3}-y^{3}\right)+3 x y(x-y)$
Solution:
Elaborating $x^{3}-y^{3}$ using the identity
$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$
$=x(x-y)\left(x^{2}+x y+y^{2}\right)+3 x y(x-y)$
Taking common x(x - y) in both the terms
$=x(x-y)\left(x^{2}+x y+y^{2}+3 y\right)$
$\therefore x\left(x^{3}-y^{3}\right)+3 x y(x-y)$
$=x(x-y)\left(x^{2}+x y+y^{2}+3 y\right)$