Question

Simplified form of expression AB + ABC is __________.

• A. AB
• B. A(B + C)
• C. A (B + A)
• D. None of the above

Answer 1

The correct option is D None of the above

In essence the method we are about to discuss is a pictorial way to apply the distributive law to factor out common subexpressions. For example:

F = AB + AB'
F = A(B + B')
F = A

Or,

F = ABC + ABC' + AB'C + AB'C'
F = A (BC + BC' + B'C + B'C')
F = A(1)
F = A

Intuitively, if you can find two terms that are equivalent except that one variable is the complement of the matching variable in the other term you can factor out this variable. The second example above shows that it works for multiple variable subsets--as long as they are powers of two.