Factorize the following expression
$8 x^{3} - 27 y^{3}$

(2 x - 3 y) (4 x^{2} + 6 x y + 9 y^{2})

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(2 x + 3 y) (4 x^{2} + 6 x y + 9 y^{2})

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(2 x - 3 y) (4 x^{2} - 6 x y + 9 y^{2})

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None of these

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Solution

The correct option is B $(2 x - 3 y) (4 x^{2} + 6 x y + 9 y^{2})$
$8 x^{3} - 27 y^{3}$

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

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

$= (2 x - 3 y) (4 x^{2} + 6 x y + 9 y^{2})$

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