First build. Will this work?

[Burgerkern]

Case - Sentey Extreme Division GS-6050 II Halcon Black SECC ATX Mid Tower Computer Case / USB 3.0 - [url]http://www.newegg.com/Product/Product.aspx?Item=N82E16811322052[/url]

Motherboard - ASRock Socket FM2/AMD A75 FCH/DDR3/A&V&GbE/SATA3&USB3.0/MicroATX Motherboard FM2A75 PRO4-M - [url]http://www.amazon.com/computers-accessories/dp/B009MBI68Q[/url]

Power Supply - RAIDMAX HYBRID 2 RX-530SS 530W ATX12V V2.2/ EPS12V SLI Ready CrossFire Ready Modular Power Supply - [url]http://www.newegg.com/Product/Product.aspx?Item=N82E16817152028[/url]

RAM - Crucial Ballistix Sport 8GB 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10600) Desktop Memory Model BLS8G3D1339DS1S00 - [url]http://www.newegg.com/Product/Product.aspx?Item=N82E16820148653[/url]

Processor - AMD A6-5400K APU 3.6Ghz Processor AD540KOKHJBOX - [url]http://www.amazon.com/gp/product/B0095VPBFY/ref=ox_sc_act_title_1?ie=UTF8&psc=1&smid=ATVPDKIKX0DER[/url]

Graphics Card - SAPPHIRE 100354OC-2L Radeon HD 7870 GHz Edition 2GB 256-bit GDDR5 PCI Express 3.0 x16 CrossFireX Support Video Card - [url]http://www.newegg.com/Product/Product.aspx?Item=N82E16814202025[/url]

[B]I plan on playing Battlefield 3 on ultra settings at 1920×1080[/B]
(if you're going to recommend any parts i'm trying to keep it under $580, it's about $560 right now)

[GiGaBiTe]

I suggest you start over with your build.

AMD APUs are designed for budget oriented machines like media machines and office machines. They aren't designed for medium to high end gaming and your GPU is going to be bottlenecked to hell.

Oh and that PSU is an IED. Go with something like Thermaltake, Antec or Silver Stone.

I'd suggest something like this:

Motherboard:
[url]http://www.newegg.com/Product/Product.aspx?Item=N82E16813130653[/url]
CPU:
[url]http://www.newegg.com/Product/Product.aspx?Item=N82E16819116782[/url]

You can use the RAM you picked out and the GPU.

[fpro]

If you just want to game, maybe a dual core intel processor (for budget) and a hd 7760 or something. APU's depend largely on the amount of ram you have.