Need help to understand a step to simplify this boolean expression

Question

Looking my professor steps to simplify a boolean expression, he went from

$$A'(B+C)(A+B)C'+B'$$

to

$$A'(B+C)BC'+B'.$$

I've been trying to understand how did he do that but I can't. Can anyone help me clarify how this step was done?

Answer 1

Simply by using distributivity. Indeed $$ A'(B+C)(A+B)C'= A'(B+C)AC' + A'(B+C)BC' $$ But now $A'A= 0$, so you can now easily conclude.