Many of you are already aware of this and have made your voices heard in the forums all over. The latest Facebook update for Android is in fact draining your battery. The good news is that Facebook is aware of this and they are working to fix it. The following is taken from their official Facebook for Android page:
Hi folks, a number of you have commented on seeing a battery drain on your device since installing the new Facebook for Android app. We have identified the bug that is causing this battery drain and are working on a fix now. As soon as the patch is ready, we will push out an update. Thanks for the quick feedback and for your patience as we get this fixed!
No word on when we can expect the update so if it is a major problem for you, sign out and shut down the application. We will update you when we hear more!