Hi all,

I am struggling with the below problem:

X(u,v) = (u - u^3 / 3 + uv^2 , v - v^3 /3 + vu^2, u^2 - v^2)

So I know the normal is defined as:

N = Xu x Xv / |Xu x Xv|

And I have calculated Xu x Xv to be: (-4uv^2 - 2u(1-v^2+u^2) , -(-2v(1-u^2+v^2) - 4vu^2) , (1 - u^2 + v^2)^2 - 4u^2*v^2))

Which looks horrible and is nowhere near as simple as the answer in my solutions
N(u; v) =
(-2u; 2v; 1 - u2 - v2) / (1 + u2 + v2)

Could someone point out if I have gone wrong or how I should go about simplifying?

Many thanks