Express without sum or multiplication (Boolean algebra)

Question

I'd like to express $AB$ just in terms of sum, I have already tried this: $(A′B+AB′)′\cdot(A+B)=AB$, but, of course, $A'B$, for example, is still multiplying.

And also, I'd like to do the reverse process, expressing $ab + a'(b+c)$ just in terms of multiplication, not a single sum operator, but I'm not getting it, trying any one of the Boole's theorems...

Which would be the correct way to express both of them just with the indicated operators?

Thanks so much everyone in advance!

Answer 1

Answered in the question comments section, by @ErickWong and @FabioSomenzi.

AB     as    (A′+B′)′.
ab+a′(b+c)    as    (ab′)′⋅(b′c′)′