Factorise:
$12 (x - 2)^{2} - 25 (x - 2) (y + 1) + 12 (y + 1)^{2}$

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Solution

$\begin{matrix} 12 {(x - 2)}^{2} - 25 (x - 2) (y + 1) + 12 {(y + 1)}^{2} & = 12 {(x - 2)}^{2} - 16 (x - 2) (y + 1) - 9 (x - 2) (y + 1) + 12 {(y + 1)}^{2} = 4 (x - 2) [3 (x - 2) - 4 (y + 1)] - 3 (y + 1) [3 (x - 2) - 4 (y + 1)] = 4 (x - 2) (3 x - 6 - 4 y - 4) - 3 (y + 1) (3 x - 6 - 4 y - 4) = [4 (x - 2) - 3 (y + 1)] (3 x - 6 - 4 y - 4) = (4 x - 8 - 3 y - 3) (3 x - 4 y - 10) = (4 x - 3 y - 11) (3 x - 4 y - 10) \end{matrix}$

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