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

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

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x^{3} + y^{3}

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x^{2} + 2 x y - y + y^{2}

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x^{2} + y^{2}

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Solution

The correct option is B $x^{3} + y^{3}$
$(x + y) (x^{2} - x y + y^{2})$
$= x (x^{2} - x y + y^{2}) + y (x^{2} - x y + y^{2})$
$= x^{3} - x^{2} y + x y^{2} + x^{2} y - x y^{2} + y^{3}$
$= x^{3} + y^{3}$

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

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

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

x^{2} + y^{2} + 2 x y

x^{2} + y^{2} - x y

x y^{2}

3 x y

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