Thank you for your explaination! That question of what else adds when multiplied was one I never heard and really added insight for me. I had been always taught to memorize these equations, but thinking about the “why” is much more fun and interesting.
It always bothers me when a lecturer pulls out a "guess" that magically ends up being the right one. Like... how can I learn from that if I don't see where that guess might have come from?!