Simplify: $(x^{2} - y^{2} + 2 x y + 1) - (x^{2} + y^{2} + 4 x y - 5)$

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Solution

Given, $(x^{2} - y^{2} + 2 x y + 1) - (x^{2} + y^{2} + 4 x y - 5)$

$= x^{2} - y^{2} + 2 x y + 1 - x^{2} - y^{2} - 4 x y + 5$

$= - 2 y^{2} - 2 x y + 6$

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