problem with simplifying the boolean function

Question

Can someone explain me why $ AB \vee A \bar B C = AB \vee AC\\$ ?

How do we get rid of $ \bar B \\$?

Answer 1

We have

\begin{align} AB \lor A\bar{B}C &= A(B \lor\bar{B}C) \end{align}

Also, $B \lor \bar{B}C$ is equal to $B \lor C$ since if $B$ is true, both expression is evaluated to be true and if $B$ is false, we then have to take the value of $C$.