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Factorisation by Regrouping Terms

Factorise the...

Question

Factorise the following:
$27 - 125 x^{3} - 135 x + 225 x^{2}$

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Solution

$27 - 125 x^{3} - 135 x + 225 x^{2}$

$= (3)^{3} - (5 x)^{3} - 3 (3) (5 x) [3 - 5 x]$

$= (3 - 5 x)^{3}$

$[∵ (a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)]$

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Factorisation by Regrouping Terms

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