Factorise: ${(x - 2 y)}^{2} + 7 (x - 2 y) + 12$

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Solution

${(x - 2 y)}^{2} + 7 (x - 2 y) + 12$

Let $t = x - 2 y$

$\Rightarrow t^{2} + 7 t + 12$

$= t^{2} + 4 t + 3 t + 12$

$= t (t + 4) + 3 (t + 4)$

$= (t + 4) (t + 3)$

$= (x - 2 y + 4) (x - 2 y + 3)$

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