The Facebook app for iOS has been the target of a lot of abuse from users lately thanks to its propensity to use more power than it should. Yesterday, Facebook pushed out a partial fix to the app and explained what was causing the battery-killing issue.
Facebook engineering manager Ari Grant noted that a "CPU spin" was discovered in networking code, making the app perform an unending process. While the app update released yesterday doesn't fix the problem totally, it does contain improvements.
But that wasn't all that was causing the problem; there was a bug in audio management that kept audio sessions open even if there was no media playing. Apple gives apps the ability to run audio in background so that users can listen to music or podcasts while performing other tasks, and Grant said that Facebook was still "awake" in background due to the bug, but wasn't performing any useful tasks. For the time being, Facebook has removed the background audio capability.
The update appeared yesterday in Facebook version 42.0, and has probably already loaded itself onto your iPhone or iPad. If not, check Updates in the App Store or download the new version of Facebook for free from the App Store.