Simplify
$3 a b - 2 a^{2} - 2 b^{2} - (5 a^{2} - 7 a b + 5 b^{2})$

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Solution

Consider $3 a b - 2 a^{2} - 2 b^{2} - (5 a^{2} - 7 a b + 5 b^{2})$
$= 3 a b - 2 a^{2} - 2 b^{2} - 5 a^{2} + 7 a b - 5 b^{2} = (- 2 a^{2} - 5 a^{2}) + (- 2 b^{2} - 5 b^{2}) + (3 a b + 7 a b) = - 7 a^{2} + (- 7 b^{2}) + (10 a b) = - 7 a^{2} - 7 b^{2} + 10 a b$
Hence, $3 a b - 2 a^{2} - 2 b^{2} - (5 a^{2} - 7 a b + 5 b^{2})$ is equal to $- 7 a^{2} - 7 b^{2} + 10 a b$

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5 a^{2} - 7 a b + 5 b^{2}

3 a b - 2 a^{2} - 2 b^{2}

5 a^{2} - 7 a b + 5 b^{2}

3 a b - 2 a^{2} - 2 b^{2}

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$5 a^{2} - 7 a b + 5 b^{2} f r o m 3 a b - 2 a^{2} - 2 b^{2}$

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