Expansion of $(3 x - 2 y)^{3}$ is

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

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

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

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None of these

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Solution

The correct option is A $27 x^{3} - 8 y^{3} - 54 x^{2} y + 36 x y^{2}$
Using $(a - b)^{3} = a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}$

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

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