Product of maxterms

Question

Please help me break the ice in understanding how we derive a product of maxterms, say, for:

$xy+x'z $

I could be missing some concept here in this but be patient with me. I have also done SOP and POS.

My domain is x,y, z. In the first term, $xy, z$ or $z'$ are missing, so I add $zz'$

and in second term $x'z$, I would add $y'y$ thus:

$(xy+zz')+(x'z+yy')$ which I I think due to a theorem, evaluates to:

$(xy+z)(xy+z')+(x'z+y)(x'z+y')$

First, I am not sure if what I have done above is on right track. Secondly, am not sure what next.

Answer 1

We have two Identities

1. Multiplicative x.x' = 0
2. Additive x+x' =1

We use these while converting to SOP or POS form. Use the simplest oone to your requirements