I am currently playing games and editing video on my macbook pro 2010 that sucks and can play l4d2 and tf2 on barely 60 on low. I wanna build a pc that can run bf3 on high and edit hd video smooth on a 850 budget (i have a razer blackmagic and deathadder so keyboard and mouse aren't necessary.)
Good for a strict gaming build, but video editing will require more than 8 gb of RAM, and depending on the Editing software, it may not be able to use 8 cores. You're giving him a build before asking enough questions.
What video editing software will you be using? This also affects the choice of video card, as some are optimized for AMD, and other are more optimized for Nvidia's CUDA.
Here is an great build for editing and with still be able to play BF3 and high at a constant 60FPS. You can either get the GTX 670, which will be about 10% better fir editing, but the Radeon HD 7950 will be a bit better in most games and is about 5% better. Personally I would go with this build with the 7950 because the i7 being hyperthreaded will preform much better with editing and will pick up the slack of the AMD GPU. http://pcpartpicker.com/p/Abb1
I strongly disagree with the RAM comment here. In a video editing machine, the amount of RAM is nearly as important as the CPU. You want enough RAM to be able to store the entire video file you're working on (as well as revisions) in system memory, and they can get considerably larger than 8gb, especially since you want to edit HD video. 16gb is the minimum I would put in a new video editing machine at this budget.
Don't buy RAM seperately for this machine. RAM from two seperate kits is fine for a gaming machine, but when you're working on a project, you want stability, which is better when all RAM is from the same kit.
The latency of the RAM in also more important to a video editing machine than it is to a gaming machine. Getting a 16gb set of CAS 8 RAM is worth the extra ~$15 over CAS9 for editing.
for video editing, it's best to buy all your RAM at once, in a single kit.