Question
How much is $x^2-2 x y+3 y^2$ less than $2 x^2-3 y^2+x y$ ?
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Answer
Required expression:
$=\left(2 x^2-3 y^2+x y\right)-\left(x^2-2 x y+3 y^2\right)$
$=2 x^2-3 y^2+x y-x^2+2 x y-3 y^2$
Collecting positive and negative like terms together, we get
$2 x^2-x^2-3 y^2-3 y^2+x y+2 x y$
$=x^2-6 y^2+3 x y$
$=\left(2 x^2-3 y^2+x y\right)-\left(x^2-2 x y+3 y^2\right)$
$=2 x^2-3 y^2+x y-x^2+2 x y-3 y^2$
Collecting positive and negative like terms together, we get
$2 x^2-x^2-3 y^2-3 y^2+x y+2 x y$
$=x^2-6 y^2+3 x y$
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