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Factorisation by Common Factors

Factorise the...

Question

Factorise the following:
$125 x^{3} - 8 y^{3}$

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Solution

$125 x^{3} - 8 y^{3}$
$= (5 x)^{3} - (2 y)^{3}$
$= (5 x - 2 y) [(5 x)^{2} + 5 x .2 y + (2 y)^{2}]$
$[a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2}]$
$= (5 x - 2 y) [25 x^{2} + 10 x y + 4 y^{2}]$

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