Question
Factorize:
$x(x^3 - y^3) + 3xy(x - y)$
$x(x^3 - y^3) + 3xy(x - y)$
✓
Answer
$x\left(x^3-y^3\right)+3 x y(x-y)$
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 $=x(x-y)\left(x^2+x y+y^2+3 y\right)$
$\therefore x\left(x^3-y^3\right)+3 x y(x-y)$
$=x(x-y)\left(x^2+x y+y^2+3 y\right)$
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 $=x(x-y)\left(x^2+x y+y^2+3 y\right)$
$\therefore x\left(x^3-y^3\right)+3 x y(x-y)$
$=x(x-y)\left(x^2+x y+y^2+3 y\right)$
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