If R is a ring of characteristic p, prove (x+y)^p = x^p + y^p for all x,y in R. We need to use the rule that for each n>= 1, (x+y)^n = (sigma, k=0 to infinity)(n choose k) x^k y^(n-k).

I truly don't know where to start other that maybe setting the summation = x^p + y^p