Hello, feage7!

I'm embarrassed . . . It's even simpler than I thought.

Note that the answer has: . $(a-b)^2(b-c)^2(a-c)^2$

Since all those factors are squared, the order of subtraction doesn't matter!

. . That is: . $(b-a)^2 = (a-b)^2$, etc.

So I didn't have to do any "switching" . . .