Question
Subtract $x^2-2 x y+5 y^2-4$ from $4 x y-5 x^2-y^2+6$.
✓
Answer
We have:
$\left(4 x y-5 x^2-y^2+6\right)-\left(x^2-2 x y+5 y^2-4\right)$
$=4 x y-5 x^2-y^2+6-x^2+2 x y-5 y^2+4$
$=-6 x^2-6 y^2+6 x y+10$
$=-2\left(3 x^2+3 y^2-3 x y-5\right)$
$\left(4 x y-5 x^2-y^2+6\right)-\left(x^2-2 x y+5 y^2-4\right)$
$=4 x y-5 x^2-y^2+6-x^2+2 x y-5 y^2+4$
$=-6 x^2-6 y^2+6 x y+10$
$=-2\left(3 x^2+3 y^2-3 x y-5\right)$
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