Matrix multiplication with dot products

Question

I was wondering about trying to factor the following expression, but I couldn't come up with anything.
$$ (A{\bf v}) \cdot (A{\bf{w}})
$$
We can't factor out the matrix $A$ because we cannot multiply a matrix with the result of a dot product as it is a scalar. Surely there is something I am missing, is there any other useful expression we can form that is equal to this?

Answer 1

Benjamin_Gal's comment answered but I am putting this to close the question.

Write $v' = Av$ and $w' = Aw$, and note that $v' \cdot w'$ can be written as $v'^T w'$.
-Benjamin_Gal's comment