Simplifying three variables boolean algebra

Question

$$F(A,B,C)= (AC+ABC')(BC+B'C')= A(C+BC')(BC+B'C')$$ What is the next step? Please help me I'm stuck

Answer 1

You can go on expanding, giving $$ (C + BC')(BC + B'C') = BCC + BCC' + BBC'C + BB'CC' $$ Now $BB' = CC' = \bot$ and $CC = C$, hence we get $$ (C + BC')(BC + B'C') = BC $$ Therefore $F(A,B,C) = ABC$.