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

- 2 x y + 6

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2 x y + 6

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

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- 2 y^{2} - 2 x y - 6

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Solution

The correct option is B $- 2 x y + 6$
Given: $(x^{2} - y^{2} + 2 x y + 1) - (x^{2} - y^{2} + 4 x y - 5)$
$= x^{2} - y^{2} + 2 x y + 1 - x^{2} + y^{2} - 4 x y + 5$
$= x^{2} - x^{2} - y^{2} + y^{2} + 2 x y - 4 x y + 1 + 5$
$= - 2 x y + 6$
$∴$ $(x^{2} - y^{2} + 2 x y + 1) - (x^{2} - y^{2} + 4 x y - 5) = - 2 x y + 6$

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