Factorise: $(1 - x^{2}) (1 - y^{2}) + 4 x y$

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Solution

$(1 - x^{2}) (1 - y^{2}) + 4 x y$

$1 - x^{2} - y^{2} + x^{2} y^{2} + 4 x y$

$(1 + 2 x y + x^{2} y^{2}) - (y^{2} + x^{2} - 2 x y)$

$(1 + x y)^{2} - (x - y)^{2}$

$(1 + x y + x - y) (1 + x y - x + y)$

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