Why China Invaded Tibet

So, I got two people asking the same question: Why did China invade Tibet? I'm not exactly sure why China invaded ALL of Tibet. I read somewhere that about two-thirds of Tibet was actually part of China at one point. Thus, China probably felt like they needed more land and invaded. Today, Tibet is split into three regions. The two regions that belonged to China - I believe U-Tsang (Central Tibet) and Amdo (Northeast Tibet) are now under China's government. The third section - Kham in the Southeast Tibet is known as the T.A.R. or Tibet Autonomous Region, which is basically a colony.