Compute $(3 m - 2 n)^{3}$

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Solution

$(3 m - 2 n)^{3}$
We know that $(x - y)^{3} = x^{3} - y^{3} - 3 x y (x - y)$
Here x=3m and y=2n we get
$∴ (3 m - 2 n)^{3}$
= $(3 m)^{3} - (2 n)^{3} - 3 (3 m) (2 n) (3 m - 2 n)$
= $27 m^{3} - 8 n^{3} - 12 m n (3 m - 2 n)$
= $27 m^{3} - 8 n^{3} - 36 m^{2} + 24 m n^{2}$
= $27 m^{3} - 36 m^{2} n + 24 m n^{2} - 36 n^{2}$

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