I'm given the following first fundamental form for a surface:
$$ds^2=(2+v^2)du^2+2(2+uv)dudv+(2+u^2)dv^2.$$
By Brioschi's Formula, the Gaussian curvature, as I've calculated it, is:
$$K=2(u-v)^2/(3u^2v^2-2u^2+16uv-2v^2+12)^2.$$
I've double checked the computation and made sure I correctly applied the formula.
The answer choices are: $0,1,uv,(u-v)^2,2(u-v)^2$.
This is not among the answer choices on this short computation assignment I was given. Perhaps there is an error among the answer choices. If this is not the correct answer, could someone demonstrate the proper way to compute it?