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

x^{3} - y^{3}

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x^{3} + y^{3}

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x^{3} + y^{3} + 3 a b

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x^{3} + y^{3} - 3 a b

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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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Verify:

(i)

(ii)

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

[\frac{x^{3} + y^{3}}{{(x - y)}^{2} + 3 x y}] \div [\frac{{(x + y)}^{2} - 3 x y}{x^{3} - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

[\frac{x^{3} + y^{3}}{(x - y)^{2} + 3 x y}] + [\frac{(x + y)^{2} - 3 x y}{x^{3} - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

[\frac{x^{3} + y^{3}}{{(x - y)}^{2} + 3 x y}] \div [\frac{{(x + y)}^{2} - 3 x y}{x 3 - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

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