As of right now, it can only simplify and is also slightly buggy. The demo multiplies two monomials/polynomials together (shows the full simplified version), but it only works for one variable. Things like (xy^2)*(x+y) is not possible. Also, x^1 just means x, and x^0 means it's a constant.
This took roughly 2 hours; longer than it should have. But I'm pretty happy with the results. A problem is that it's not very fast, which might not matter now, but probably will as I develop it.