If $(1 - x^{2}) (1 - y^{2}) + 4 x y$ factorized then its factors are

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Solution

Given that function

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

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

$\Rightarrow x^{2} y^{2} + 1 - x^{2} - y^{2} + 2 x y + 2 x y$

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

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

$\Rightarrow$ We know that $∵ (a^{2} - b^{2}) = (a + b) (a - b)$

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

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

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