Work sth out
If you work something out, you solve a problem or an issue
E.g. Please don’t cry. We will work this out, I promise.
If you work out something, you calculate or assess how to do it
E.g. Can you work out how to get to the station as soon as possible?
If you work something up, you develop a plan or idea by taking all the details into account
E.g. The committee promised to work up proposals for improving the current traffic congestion issue in the city.
Work on sb
If you work on somebody, you are trying to persuade this person to do something
E.g. I am working on my parents to get them to buy a new phone for me.
Work sb over
If you work somebody over, you attack and injure them
E.g. He was assaulted yesterday night and God, he was worked over pretty good.
If you work emotions up, you raise them and cause excitement
E.g. He worked up the public’s passions to rage.