Can Boolean Algebra Simplify Complex Expressions Using Postulates and Theorems?

[physics=world]

1. Simplify the expression:

F = xyz' + xy'z' + x'yz + xyz2. Postulates and theorems

The Attempt at a Solution

F = xyz' + xy'z' + x'yz + xyz

= x(yz' + y'z') + yz(x' + x) (Distributive)

= x(yz' + y'z') + yz.1 (Complement)

= x(yz' + y'z') + yz (identity)

This is where I need help.

 

[axmls]

Notice that you can factor the z' out of the first term.