Has knowing those factorisations come in handy?
Not at all. Do you think I would stuff my primitive cerebrum with the mere memorization of identities? But the looking up of them when necessary has been a great help.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.