I have this kind of problem:

(1): Let k,m,l be cardinals. Prove that k(m+l)=km+lm.

I know, that I have to prove that there exist a bijection between Kx(LuM) and

(KxL)u(KxM) where card(K) = k, card(L) = l and card(M) = m, but how I do it?

I'm little bit lost here, can anyone help?