function field of projective plane isomorphic to function field of product of projective line

Question

I need to show that given a projective plane $P^{2}$ and product of projective line $P^{1}\times P^{1}$,their function field are isomorphic. However, what is the proper definition of function field $k(P^{1}\times P^{1})$? Since it cannot be direct product of $k(P^{1})\times k(P^{1})$. Should it be direct sum of fields? And how are they isomorphic to each other?