Factorise: $(x + y)^{2} - 4 x y$

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Solution

We need to factorise $(x + y)^{2} - 4 x y$
It can be written as $(x + y)^{2} - 4 x y = (x + y)^{2} - (2 \sqrt{x y})^{2}$
$= (x + y - 2 \sqrt{x y}) (x + y + 2 \sqrt{x y})$
Thus factors are $(x + y - 2 \sqrt{x y}), (x + y + 2 \sqrt{x y})$ .

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