For one of the inclass problems, we had to prove the following statment using Properties of Boolean Algebra:
xyz + x'y'z + x'yz + xyz' + x'y'z' = xy + yz + x'y'
My professor first grouped the terms on the left hand so Complement Rule can be used:
= xyz + xyz' + x'yz + x'y'z + x'y'z' = xy( z + z') + ( x + x') yz + x'y' (z+z')
I don't understand where the additional x came from ?
It may help to note that $xyz$ is the same as $xyz + xyz$.
So work with $xyz + xyz + x'y'z + x'yz + xyz' + x'y'z'$ and you will get your result.