Trying to simplify boolean algebra a+ac+ab

Question

I am trying to simplify A+AC+AB. I think I have solved it, but I want to double check its right, can it be simplified to A+A(C+b) and then again to A(C+B) as A+A = A?

Answer 1

$$\begin{align} A+AC+AB & = A1+AC+AB \\ & = A(1+C+B) \\ & = A(1) \\ & = A \end{align}$$

Instead of doing $A+A=1$ you can use distributive law as you can see above in the second step.

Note: You have simplified the expression to $A(C+B)$ but the simplest form is $A$.