I need to simplify the following expression: $$a'·b·(a'+c)+a·b'·(b'+ c)$$
The problem is that when I try it, I end up with a $0$ multiplying the expression, so everything becomes cero. I get confused with the parentheses in the addition, and I've asked in some other forums but everyone gets different answers.
Thanks in advance.
Given expression, $$ a' \cdot b( a' + c) + a \cdot b' \cdot ( b' + c) $$ $$ = a' \cdot b \cdot a' + a' \cdot b \cdot c + a \cdot b' \cdot b' + a \cdot b' \cdot c$$ $$ = a' \cdot b + a \cdot b' + a' \cdot b \cdot c + a \cdot b' \cdot c $$ $$ ( a' \cdot b + a \cdot b')\cdot ( c + 1) = a' \cdot b + a \cdot b' $$
It can be verified from here .