In Maple it is possible to definedefine a multilinear, orderless operator with:
define(A,'orderless',multilinear): I can't seem to find the equivalent in Mathematica.
I would like it to do something like:
A[x,x]/.x->0+bx+cx^2>0+b x+c x^2 (* b^2 A[x,x]+2 b c A[x, x^2]+c^2 A[x^2,x^2] *)