I've never done this type of Algebra... and it's a bit confusing. I've completed this question, but I don't know if I took the right steps...

*=AND, +=OR, '=NOT

If A*B = 0, A+B=1

Prove: (A+C)*(A'+B)*(B+C) = B*C

I expanded it a bit and applied some of the rules. Can someone explain it step by step? I got the answer but I'm a bit confused at how I got the answer.

Thanks!