f(x+y,xy)
=f(u,v)
=2x^2 + 3xy + 2y^2 + 6
=2(x^2 + 2xy + y^2) - xy + 6
=2(x+y)^2 - xy + 6
=2u^2 - v + 6
As you can see, if the f(u, v) function equation uses X and Y to represent two independent variables, then its expression will become:
f(x,y) = 2x^2 - y + 6