I am wondering how this development is made. I would be really greatful if anyone would like to explain that to me. I don't understand why the right side wont have the form of the product rule like you could see the left side has. This is all from a proof of Leibniz formula by the way.
\begin{align} &\sum_{k=0}^{p-1}{p-1 \choose k}{D^{p-k}fD^{k}g + \sum_{l=1}^{p}{p-1 \choose l-1}{D^{p-l}fD^{l}g} =\\{D^{p}fg} +\sum_{k=1}^{p-1}[{p-1 \choose k}+{p-1 \choose k-1}]{D^{p-k}fD^{k}g+f{D^{p}g}}}. \end{align}
Thank you!