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

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Solution

Consider $(x + y) (x^{2} - x y + y^{2})$
$x (x^{2} - x y + y^{2}) + y (x^{2} - x y + y^{2}) x^{3} - x^{2} y + x y^{2} + y x^{2} - x y^{2} + y^{3} x^{3} - y^{3}$
Hence, $(x + y) (x^{2} - x y + y^{2})$ is $x^{3} - y^{3}$

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