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

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Solution

Let $α = x - 2 y$ then
$= α^{2} + 7 α + 12$
$= α^{2} + 4 α + 3 α + 12$
$= (α + 4) (α + 3)$
$= (x - 2 y + 4) (x - 2 y + 3)$ where $α = x - 2 y$

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