The expression $27 x^{3} + 8 y^{3}$ can be expressed in factors as

(3 x - 2 y)^{3}

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(3 x + 2 y)^{3}

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(2 x + 3 y)^{3}

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None of these

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Solution

The correct option is D None of these
Given, $27 x^{3} + 8 y^{3}$
$= (3 x)^{3} + (2 y)^{3}$
Since, $a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$
$\Rightarrow (3 x)^{3} + (2 y)^{3} = (3 x + 2 y) [(3 x)^{2} + (2 y)^{2} - (3 x) (2 y)]$
$= (3 x + 2 y) (9 x^{2} + 4 y^{2} - 6 x y)$
Option D is correct.

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