Faulty Syllogism
Major Premise: Some people from Boston are Patriot fans.
Minor Premise: Mike is from boston.
Conclusion: Mike is a Patriots fan.
Explanation: This is a faulty Syllogism because even though Mike is from Boston, it is possible that Mike isn't a Patriots fan.

Vaild Syllogism 
Major Premise: There are 5,280 feet in a mile.
Minor Premise: Eric walked for a mile.
Conclusion: Eric walked for 5,280 feet.
Explanation: This is a valid syllogism because there are 5,280 feet in a mile, and since Eric walked for a mile, He walked for 5,280 feet.

A Syllogism Embedded in an argument.
Fraternity Boys are loud, drink lots of beer and, cause many problems for a University. Joe, a Fraternity Boy, just moved in next door into an apartment.Therefore, Joe is going to be a bad neighbor and be loud, drink lots of beer, and cause many problems.

Explanation: This is a invalid syllogism in an argument becuase it is possible that Joe could be a good neighbor and not cause any issues with the residents at the apartment.