So if I say I don't like tomatoes, that would just require adding "Nie" right?
Nie lubię pomidory.
no. it also needs change is cases, accusative->genitive.
Lubię pomidory- nie lubię pomidorów.
Why the genitive case? I thought that indicated possession (of the)
Genitive has many functions. Apart from possession (like "George's car" or "the house of the headmaster") it also is needed when you negate a sentence that took Accusative. Note that only Accusative changes the case when negated.
This is what's fun learning a new language. Polish is kewl!
Is pomidory in the accusative case here?
You are correct, it's an accusative.