Factorise:

$4 (2 x - 3 y)^{2} - 8 x + 12 y - 3$

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Solution

$4 (2 x - 3 y)^{2} - 8 x + 12 y - 3 l e t 2 x - 3 y = a 4 (2 x - 3 y)^{2} - 8 x + 12 y - 3 \Rightarrow 4 a^{2} - 4 a - 3 \Rightarrow 4 a^{2} - 6 a + 2 a - 3 \Rightarrow 2 a (2 a - 3) + 1 (2 a - 3) \Rightarrow (2 a - 3) (2 a + 1) \Rightarrow (2 (2 x - 3 y) - 3) (2 (2 x - 3 y) + 1) \Rightarrow (4 x - 6 y - 3) (4 x - 6 y + 1)$

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