  In this note, we prove that if $A$ is a finite set of real numbers such that
$|AA| = K|A|$, then for every polynomial $f \in \mathbb{R}[x,y]$ we have that
$|f(A,A)| = \Omega_{K,\operatorname{deg} f}(|A|^2)$, unless $f$ is of the form
$f(x,y) = g(M(x,y))$ for some monomial $M$ and some univariate polynomial $g$.
