let F be a field with characteristic p, a prime. show that (a+b)^p = a^p + b^p for all a,b in F.

Using pascal's triangle it's easy to show for the first few primes that this is true, yet I don't know how to prove it for all primes, p. I was thinking of using induction, but don't know exactly how to go about doing that. Any help would be appreciated.