I am trying to get a lower bound on $|A+AA|$ where $A$ is a set, and $A+AA=\{a+bc: a,b,c \in A\}$ using Szemeredi Trotter.
I would think we need to form lines of the form $y=ax+b$ where $a,b \in A$, but I'm not sure what to let be the "points" in this situation so that we can apply the inequality: $I(P,L) \leq (PL)^{2/3}+P+L$.
Thank you!