One of the factor of $81 x^{3} + 192 (- y)^{3}$ is

9 x^{2} - 12 x y + 16 y^{2}

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9 x^{2} + 24 x y + 16 y^{2}

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9 x^{2} - 24 x y + 16 y^{2}

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27 x^{2} + 36 x y + 48 y^{2}

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Solution

The correct option is D $27 x^{2} + 36 x y + 48 y^{2}$
We have,
$81 x^{3} - 192 y^{3}$
$\Rightarrow 3 (3 x)^{3} - 3 (4 y)^{3}$

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

Therefore,
$\Rightarrow 3 (3 x - 4 y) (9 x^{2} + 12 x y + 16 y^{2})$
$\Rightarrow (3 x - 4 y) (27 x^{2} + 36 x y + 48 y^{2})$

Hence, this is the answer.

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