There is a certain matrix operation that I've seen performed in several proofs/derivations, but I've never been able to find a clear rule for it. I'm not even sure how to search for it online. It looks like this:
A + BCD = B(A + C)D
For a working example, see (eq. 1) here.
Under what conditions is this true? Do A, B, and/or D have to meet some criteria? Is there a rule for this that I've missed somewhere? It seems like there would be, given the number of times I've encountered it.