My professor gave us this query at the end of class, and I started thinking about axioms, but I didn't think of anything that would have to make the following statement true. Thoughts?

What must be true about a nontrivial commutative ring R in order to conclude

(a+b)^4 = a^4 + 2a^2b^2 + b^4 for all elements a and b in R?

Clarification would be great on this one.