How to multiply these summations ?

Ok. I feel a little dumb for asking, but I'm working on a abstract algebra proof and this has got me stuck:

$\left(\sum_{i=1}^{n}a_ib_i\right)\left(\sum_{i=1}^{k}a_ib_i\right)$ where n,k are some positive integers.

I feel certain that it's not just a sum to n+k or nk, but I could be wrong. any help would be awesome. :)