Hello guys I was just wondering how you guys deal with the trolls early on in Baldur's Gate 2 like the ones found in the quest de'Arnise keep or some of the other side quests that have you fighting trolls. I always have problems getting the trolls to stay dead unless I buy the sword with fire at the adventurer's mart but as it is fairly expensive early on I always have to wait and spend most of my money on it. Also in playthroughs where my main character doesn't use longswords it makes the sword a much less attractive purchase.

So my question is am I going about this the wrong way? Should I be using mage spells to finish off the trolls or should I buy a bunch of fire arrows to make this easier for me?

There isn't really a "right" way. Fire or poison arrows work pretty well. Low-level mage and druid spells also do the trick.
Just save the spells and arrows until the trolls are down, so you have some backup just in case.

This hopefully is not much of a spoiler, but as I recall, there are plenty of fire and acid arrows available as treasure in de'Arnise Keep. Enough that you probably do not need to buy any, as long as you hit all the treasures and conserve the arrows.

To conserve the arrows, only use them as the finishing shot on a down troll. When a troll goes down, pause. Select your archer. I think it's a right-click on the bow and you get to choose the ammunition. Choose your fire or acid arrow, target the down troll. When the troll dies (and if you have auto-pause when target dies, that helps), click on your archer, click the bow, choose another ammunition.

Conserve the arrows in that way, and you should have plenty to finish the Keep without buying more arrows.

What Gromuhl said. You can find a few scores of fire and acid arrows early on in the keep itself in the armory where you meet Daelson, and I think if you speak with the guard captain before entering the keep he will also give you a few arrows.

IIRC, there are a ton of fire and acid arrows in the keep itself. Other than that though, Melf's Acid Arrow is probably going to be your spell of choice for all of that dungeon.

The level 3 spell 'Melf's Minute Meteors' will finish them off for you.

After you finish the slaver quest in the Copper Coronet, Bernard sells a +3 axe that does fire damage. It's fairly cheap, too, especially considering how strong it is and how early you can get it. It's an excellent weapon against trolls, but honestly it's worth using all the time if you have anyone with an axe proficiency. Other than that, arrows are your best bet.

Trolls can be tricky. There are different ways of dealing with them. This vid may help with some:

Linkypoo