I leverage the structure of commutative groups to reformulate traditional difference-in-differences (DiD) expressions into a Difference-of-Sums (DoS). This algebraic restructuring yields equivalent results while reducing the number of -'' symbols by approximately 66\%. Furthermore, I demonstrate that DoS attains the lower bound on the number of -'' symbols among all expressions equivalent to DiD. While this article is generally tongue-(in+cheek), I demonstrate that the rewritten expression can meaningfully simplify the interpretation of validity assumptions.