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Addition of Rational Expressions

Simplify2x2-y...

Question

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

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Solution

Consider $2 x^{2} - y^{2} + 2 x y - (5 x^{2} - y^{2} + 4 x y)$
$= 2 x^{2} - y^{2} + 2 x y - 5 x^{2} + y^{2} - 4 x y = (2 x^{2} - 5 x^{2}) + (- y^{2} + y^{2}) + (2 x y - 4 x y) = - 3 x^{2} + (0) + (- 2 x y) = - 3 x^{2} - 2 x y$
Hence, $2 x^{2} - y^{2} + 2 x y - (5 x^{2} - y^{2} + 4 x y)$ is equal to $- 3 x^{2} - 2 x y$

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