Find the cube of : $3 a - 2 b$

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

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

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

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Solution

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

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