You can put this solution on YOUR website! I guess this is the vertical method (using .... to keep things lined up):
:
........................................m^2 - 5mn + 3n^2
........................................m^2 + 4mn - 2n^2
.................----------------------------------
............................-2m^2n^2 + 10mn^3 - 6n^4
............4m^3n - 20m^2n^2 + 12mn^3
m^4 - 5m^3n + 3m^2n^2
--------------------------------------------
m^4 - m^3n - 19m^2n^2 + 22mn^3 - 6mn^4
:
Check this carefully a great chance for error here.