Find the cube of $3 a - 2 b$

27 a^{3} - 54 a^{2} b + 36 a b^{2} - 8 b^{3}

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a^{3} - 54 a^{2} b + 6 a b^{2} - b^{3}

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27 a^{3} - 54 a^{2} b + 6 a b^{2} - 8 b^{3}

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a^{3} - 54 a^{2} b - 36 a b^{2} - 8 b^{3}

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Solution

The correct option is A $27 a^{3} - 54 a^{2} b + 36 a b^{2} - 8 b^{3}$
$3 a - 2 b$
Cubing, we get
$= (3 a - 2 b)^{3}$
Using, $(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$
$= (3 a)^{3} - 3 (3 a)^{2} (2 b) + 3 (3 a) (2 b)^{2} - (2 b)^{3}$
$= 27 a^{3} - 54 a^{2} b + 36 a b^{2} - 8 b^{3}$

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