Form the sum of $3 x^{2} + 2^{2}, - x^{2} - 4 y^{2} + 4 x y$ and $6 x y + 2 x^{2} - 3 y^{2}$ subtract $- 5 x^{2} + 2 y^{2} - 3 x y$

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Solution

$(3 x^{2} + 2^{2}) + (- x^{2} - 4 y^{2} + 4 x y) + (6 x y + 2 x^{2} - 3 y^{2}) - (- 5 x^{2} + 2 y^{2} - 3 x y)$
$= (4 x^{2} - 7 y^{2} + 10 x y + 4) - (- 5 x^{2} + 2 y^{2} - 3 x y)$
$= 9 x^{2} - 9 y^{2} + 13 x y + 4$

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What should be subtracted from 2 x^{2} - 4 y^{2} + 6 x y + 10 to obtain - 2 x^{2} - 3 y^{2} + 6 x y + 10 ?

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