# Math Help - Simplify the expression using Boolean algebra?

1. ## Simplify the expression using Boolean algebra?

(AB+AC)(B+C)+ABD

First, I factored the A out:

A(B+C)(B+C)+ABD

x.x=x, so:

A(B+C)+ABD

Now I am stuck. Any suggestion on the next step to take?

2. Now expand :

A(B+C)+ABD
AB + AC + ABD
[AB + ABD] + AC //Use the identity X + XY = X + Y

3. Originally Posted by Mattpd
(AB+AC)(B+C)+ABD

First, I factored the A out:

A(B+C)(B+C)+ABD

x.x=x, so:

A(B+C)+ABD

Now I am stuck. Any suggestion on the next step to take?
I have to nitpick when the word 'simplify' appears. I think it is not well defined....

The word 'simplify' is especially not well defined for Boolean Algebra. The questions should be of the form prove one expression is another. Certain awful looking expressions in minterm expansion look compact in the maxterm expansions.

A(B'+C') + AB'D = AB'(1 + D) + AC' = AB' + AC' = A(B'+C') = A(BC)' = (A' + BC)'

You see, all the three expressions (namely A(B'+C'), A(BC)', (A' + BC)' ) are equal. So how do we decide which is "simple"?