Factorise the following :
i) $3 - 12 (a - b)^{2}$
ii) $4 a^{2} - 9 b^{2} - 2 a - 3 b$

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Solution

(1)
$3 - 12 {(a - b)}^{2}$

$= 3 {1 - 4 {(a - b)}^{2}}$

$= 3 {{(1)}^{2} - {(2 a - 2 b)}^{2}}$

$= 3 [1 + (2 a - 2 b)] [1 - (2 a - 2 b)]$ ( By applying $x^{2} - y^{2} = (x + y) (x - y)$ )

$= 3 (1 + 2 a - 2 b) (1 - 2 a + 2 b)$

(2)
$4 a^{2} - 9 b^{2} - 2 a - 3 b$

$= {(2 a)^{2} - (3 b)^{2}} - 2 a - 3 b$

$= (2 a + 3 b) (2 a - 3 b) - (2 a + 3 b)$ ( By applying $x^{2} - y^{2} = (x + y) (x - y)$ )

$= (2 a + 3 b) (2 a - 3 b - 1)$

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