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

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Solution

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

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

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

$= x^{3} - y^{3}$

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