My problem is the following:
Let $p$ be a non constant polynomial over $\mathbb {R}$ and define $F(x,y)=(p(x+y),p(x-y))$.Show that $DF(x,y)$ is invertible in a dense and open subset of $\mathbb {R^2}$.
I've been thinking a lot on this one, but couldn't get far... I'm really stuck... any help is much appreciated!