This would be a better match and is this the kit that you had purchased.
I bought a 4gb kit but the part number in CPU-Z shows the part number as F3-10666CL9-2GBNS and when I look up it on newegg it shows the ram in the original post. I want to upgrade my ram because BF3 maps load really slow with 4GB of ram and I also have trouble alt tabbing out of BF3
You will not get any benefit from adding 8gb of ram you would only need to add 4gb because the game will not use more then that.
You can try overclocking the cpu a bit and also the video card. Adding a second video card will help and by adding a SSD for the OS will help in loading maps but not in actual game play.
At this point your best option would be to get a SSD and load your OS on it but if you can't afford it then try adding just the 4gb of ram or overclocking your cpu.