Well, since (s-1)^2 shares the s^2 and the -2s and +1 terms with RHS, the only lag would be +1, so you add that.

Or s^2-2s=s(s-1) - s. So to make it into a full square, i.e, s(s-1) - 1(s-1) = s(s-1) - s +1, so we have to subtract 1 from the LHS, i.e add 1 to the RHS.

Is this the kind of answer you are looking for?