The value of $(2 x + 3 y)^{3}$ is __________.

$18 x^{3} + 27 y^{3} + 36 x^{2} y + 54 x y^{2}$

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$8 x^{3} - 27 y^{2} - 36 x^{2} y + 54 x y^{2}$

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$8 x^{3} + 27 y^{3} + 36 x^{2} y + 54 x y^{2}$

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$8 x^{3} + 36 y^{3} + 36 x^{2} y + 54 x y^{2}$

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Solution

The correct option is C
$8 x^{3} + 27 y^{3} + 36 x^{2} y + 54 x y^{2}$

We know the identity,
$(a + b)^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$

$(2 x + 3 y)^{3} = (2 x)^{3} + (3 y)^{3} + 3 (2 x)^{2} \times (3 y) + 3 \times (2 x) \times (3 y)^{2}$

= $8 x^{3} + 27 y^{3} + 36 x^{2} y + 54 x y^{2}$

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