I'm trying to work out what working is required to get from this 9 term expression:

A'BC'D + A'BCD' + A'BCD + AB'C'D + ABC'D + AB'CD' + AB'CD + ABCD' + ABCD

to this term:

AC + AD + BC + BD

In my attempts, I have been able to reduce it down to BD + AC + ABCD but I'm not sure how to split up the 4 variable term into AD + BC.

From the start, I cancelled out the 1st term with the 6th, and the 2nd term with the 4th leaving me with: A'BCD + ABC'D + AB'CD + ABCD' + ABCD

In the new expression with 5 terms, I was able to reduce down A'BCD + ABC'D to BD and AB'CD + ABCD' to AC. Unfortunately I'm still left with ABCD at the end so am wondering what rule(s) of algebra I might be missing

Any help would be greatly appreciated