Find the value
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

$=x(x-y)\left(x^{2}+x y+y^{2}+3 y\right)$

$\therefore x\left(x^{3}-y^{3}\right)+3 x y(x-y)$

$=x(x-y)\left(x^{2}+x y+y^{2}+3 y\right)$