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

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Solution

Given expression is $(x + y)^{2} - (x - y)^{2}$
By using identity $a^{2} - b^{2} = (a - b) (a + b)$
Here $a = x + y, b = x - y$
Therefore, $(x + y)^{2} - (x - y)^{2} = (x + y + x - y) (x + y - x + y)$ $= 2 x \times 2 y = 4 x y$
Thus factors are $2, 2, x, y$ .

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