Factorise: $12 x^{2} + 8 x - 4$

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Solution

$12 x^{2} + 8 x - 4$
$= 4 (3 x^{2} + 2 x - 1)$
$= 4 (3 x^{2} + 3 x - x - 1)$
$= 4 (3 x (x + 1) - 1 (x + 1))$
$= 4 (3 x - 1) (x + 1)$
$∴ 12 x^{2} + 8 x - 4 = 4 (3 x - 1) (x + 1)$

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