Factorize the following expression
$x^{3} - 8 y^{3}$

(x - 2 y) (x^{2} + 2 x y + 4 y^{2})

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(x + 2 y) (x^{2} + 2 x y + 4 y^{2})

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(x - 2 y) (x^{2} - 2 x y + 4 y^{2})

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None of these

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Solution

The correct option is A $(x - 2 y) (x^{2} + 2 x y + 4 y^{2})$
$x^{3} - 8 y$

Using $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

Let
$a = x$ $b = 2 y$

Then from the identity, we get

$= (x - 2 y) (x^{2} + 2 x y + 4 y^{2})$

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