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Factorisation by Regrouping Terms

Factorise the...

Question

Factorise the following:
$27 a^{3} - 8 b^{3} - 54 a^{2} b + 36 a b^{2}$

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Solution

$27 a^{3} - 8 b^{3} - 54 a^{2} b + 36 a b^{2}$
$= (3 a)^{3} - (2 b)^{3} - 3 (3 a) (2 b) [3 a - 2 b]$
$= (3 a - 2 b)^{3}$
$[∵ (a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)]$

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Factorisation by Regrouping Terms

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