OK, thanks heaps - I didn't realise that it was that easy...I thought there was some other process a little more mathematical!!!!
Denis' method is quite mathematical, consider this version of what you're doing:
. Now let
. Then Denis' factoring is the same as doing this, only his "drop the ys then do it with x" is secretly this factorization, and hiding the substitution of a single variable for the expression
which is essentially him overloading the x. Then the whole "putting the ys back in" is exactly multiplying back through and using yz=x.