What must be added to algebraic expression $2 a^{2} - 7 a b + 5 b^{2}$ to get $a^{2} + 4 a b - 3 b^{2}$ ?

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Solution

To obtain the required expression, we have to subtract $2 a^{2} - 7 a b + 5 b^{2} f r o m a^{2} + 4 a b - 3 b^{2}$
$a^{2} + 4 a b - 3 b^{2} 2 a^{2} - 7 a b + 5 b^{2} - + -- a^{2} + 11 a b - 8 b^{2}_$ (changing the sign of each term)
Therefore, the required expression is $- a^{2} + 11 a b - 8 b^{2}$ .

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