The image below is from an online algebra quiz I did recently for uni. I got this question wrong and it indicated what the correct answer was, however I cannot understand how they got to this answer.
This is what I came up with when working out the question:
$\frac{(3x^3-2x^2y+3xy^2-5y^3)-(2x^3+2x^2y-3xy^2-2y^3)}{x - y}$
$=\frac{x^3-4x^2y+6xy^2-3y^3}{x-y}$
$=\frac{x^2(x-4y)+3y^2(2x-y)}{x-y}$
Then from here I realised I couldn't simplify any further and so answered 'None of the above'.
Should my answer have been marked correct or is there a way to get the answer that has been provided in the yellow box in the picture?
Any help would be appreciated.
\begin{eqnarray*} x^3-4x^2y+6xy^2-3y^3 &=& x^3-y^3 -2y(y^2-3xy+2x^2)\\ &=& (x-y)(x^2+xy+y^2)-2y(y-x)(y-2x)\\ &=& (x-y)(x^2+xy+y^2+2y^2-4xy)\\ &=& (x-y)(x^2-3xy+3y^2) \end{eqnarray*}
So we have
$$...=\frac{x^3-4x^2y+6xy^2-3y^3}{x-y} ={(x-y)(x^2-3xy+3y^2)\over x-y}=x^2-3xy+3y^2$$