Let $f $ be $C^{\infty}$ with $f(x,0)=f(0,y)=0\in\mathbb R$. Show $f(x,y) = xyg(x,y)$ for $g\in C^\infty$
$f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$