Expand ${(2 a - 3 b)}^{3}$ .

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Solution

${(2 a - 3 b)}^{3}$
Using the formula ${(x - y)}^{3} = x^{3} - y^{3} - 3 x y (x - y)$ ,
${(2 a - 3 b)}^{3} = (2 a)^{3} - {(3 b)}^{3} - 3 (2 a) (3 b) (2 a - 3 b)$
$= 8 a^{3} - 27 b^{3} - 18 a b (2 a - 3 b)$
Or
$= 8 a^{3} - 27 b^{3} - 36 a^{2} b + 54 a b^{2}$ .

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