Is $f(x, y) = 0x + 0y = 0$ the only implicit homeomorphic to $\mathbb{R}^2$?

Question

Most of the time, implicits give you curves, for example $x^2 + y^2 = R^2$ or points $x^2 + y^2 = 0$.

The expression in the title is always satisfied so it spits out $\mathbb{R}^2$, is there any other expression that also spits out $\mathbb{R}^2$?