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

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Solution

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

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

$= x^{4} + 3 x^{3} y + 3 x^{2} y^{2} + x y^{3} - 3 x^{3} y - 3 x^{2} y^{2}$

$= x^{4} + x y^{3}$

$= x (x^{3} + y^{3})$

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