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Expression Formation

What would be...

Question

What would be subtracted from $x^{2} - x y + y^{2} - x + y + 3$ to obtain $- x^{2} + 3 y^{2} - 4 x y + 1$ ?

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Solution

Let m should be subtracted from $x^{2} - x y + y^{2} - x + y + 3$ to obtain $- x^{2} + 3 y^{2} - 4 x y + 1$
$x^{2} - x y + y^{2} - x + y + 3 - m = - x^{2} + 3 y^{2} - 4 x y + 1$
$m = x^{2} - x y + y^{2} - x + y + 3 + x^{2} - 3 y^{2} + 4 x y - 1$
$m = 2 x^{2} - 2 y^{2} + 3 x y - x + y + 2$

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