Question
Factorize:
$x\left(x^3-y^3\right)+3 x y(x-y)$
$x\left(x^3-y^3\right)+3 x y(x-y)$
✓
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 $\mathrm{x}(\mathrm{x}-\mathrm{y})$ 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 $\mathrm{x}(\mathrm{x}-\mathrm{y})$ 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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