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

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Solution

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

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

$= x^{3} - x^{2} y + x y^{2} + x^{2} y - x y^{2} + y^{3}$ like terms with opposite signs get cancelled.

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

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