The equation give in S = X'YZ + XZ + XY'Z + Y'Z + XY and I have to reduce it.
As my professor reduces it it goes to S=X'YZ + XZ + YZ + XY'Z + Y'Z + XY (He consensus terms 1 and 2)
and next he goes down and the equation is S = XZ + YZ +XYZ' +Y'Z + XY.
Where does the X'YZ go to? Is it absorption or something else?

 

It seems like he is going about it the long way. The solution can be had in just three or four simple steps.

HINT: Don't forget that OR distributes over AND. Thus, AB+C = AC + BC

As for where the X'YZ goes, consider the first and third terms in the prior reduction.