I have good luck eradicating most types of invasive things with a thick layer of newspaper (10-12 sheets) then some mulch. The paper will eventually break down, and in the mean time, any weeds that do manage to find their way through are very easy to pull, as the mulch helps keeps the soil moist.

If this plant sets seed, be sure to pull it or cut it off before the seeds have a chance to mature.

Another thing that helps, is to plant the plants you DO want very thickly, so they help crowd out the ones you don't want. If there is concern about bothering your plants when pulling the weeds, take a small scissors to them, or hand pruners if they are tough. Eventually the weeds will be starved out, if they keep getting lopped off.

But then again, I seem to have trouble getting my aegopodium (goutweed) to fill in thoroughly where I planted it! So, maybe invasive plants just die willingly for me!

Thanks "cantstopgardening" for your comments.
Unfortunately, these buttercups are a lot tougher than you can imagine! They are along the lines of a very tough dandelion or goutweed to kill. If you don't remove or kill all the roots they'll keep returning. Also they spread by runners and seeding themselves.
The newspaper idea might help smother them, but mulching is just what they don't need. The love moisture and acid soil.

Incidently, I also have big patches of very healthy goutweed, growing where I want it to. Our soil here is acidic, some parts are dry and some are moist.

Joan
N. Ontario

I have this 'lovely' little weed in my yard as well, talk about tough to get rid of! Occasionaly I think I'll just leave it, but after seeing how quickly it takes over I realize you have to keep on top of it. I did find a chemical that is supposed to kill it, a few ounces cost me $25 but I have yet to use it, I've just been trying to pick it out by hand and waiting for some warmer weather to try the weed killer. I am going to try a method I heard about a while ago, you make up your weed killer quite strong, then using a rubber glove on your hand you dip your fingers into the weed killer and then wipe the solution onto the individual plant that you want to kill, that way you don't kill other plants around it that you want to keep. I suppose you could also use a little brush and paint it onto the stuff you are killing. It sounds a little tedious, but I'm willing to try it, figure it'll be a good way to spend a lazy afternoon in the sun!

I have a huge issue, my yard, flowerbeds, garden ect are infested with this darn plant. I cant use any normal chemicals because I also have 4 dogs. One of my freinds owns horses, and they use a product called Ally/Cimarron to kill it. It is extreammly toxic to horses, and she said there is no wait time, after spraying, the horses can return to the feild the next day. She did tell me that you cannot put it on newly planted lawns, and that it can cause some "Bald Spots" on new growth, but at this point, Im willing to have a dirt yard to get rid of this crap! Im doing it next weekend, and I'll let ya know how it works. Wish me luck-