Simplify $x {(x - y)}^{3} + 3 x^{2} y (x - y)$

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Solution

x $(x - y)^{3}$ + $3 x^{2} y$ $(x - y)$
taking $x (x - y)$ as common
= $x (x - y) [(x - y)^{2} + 3 x y] =$ $x (x - y) [x^{2} + y^{2} - 2 x y + 3 x y]$
= $x (x - y) [x^{2} + y^{2} + x y] =$ $x (x - y) (x^{2} + y^{2} + x y)$

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