Digital logic - Boolean algebra simplification problem

[theBEAST]

Homework Statement

Simplify (A+B')(B+C)

The Attempt at a Solution

I first expanded it and got
= AB + AC + B'B + B'C
= AB + AC + B'C

Turns out the solution is AB + B'C (according to an online source). How do we get rid of the AC term?

 

[NascentOxygen]

On examining the expression, you can see ...
If B is true, then for the expression to be true, the only condition that need be met is that A is true, and it doesn't matter what C is.

If B is false, then for the expression to be true all we need is that C is true, it doesn't matter what A is.

Just as in algebra you can multiply any term by 1 and you don't change its value, then in Boolean algebra you can multiply a term by true and you change nothing.

For example, (B+B') is true, and it's always true.

AB + AC(B+B') + B'C

expand this out, then simpify the result