Let $k$ be a a field and consider the space $k[x] \otimes_k k[x]$. I would like to verify the equation
$ \sum_{k=0}^{m+n} {m+n \choose k} x^k \otimes x^{(n+m)-k}= \sum_{i=0}^n \sum_{j=0}^m{n \choose i}{m \choose j} x^{i+j}\otimes x^{(n+m)-(i+j)}$
however I am not getting very far with this. Could anyone give me some help? Thanks very much.