Of course He did, it's recorded in 3 of the 4 gospels the He exorcised demons quite frequently, and He even empowered others to exorcise demons. Indeed people exorcise demons in His name to this day. Just because the gospel of John doesn't mention Him exorcising demons doesn't mean there's any sort of discrepancy - he simply didn't feel a need to include it because he was more focused on the nature of Jesus than His specific actions.
As far as I am aware there are no contradictions on the Bible. People often point to the sorts of cases claiming a contradiction, when really it is two authors describing different aspects of a thing that are all simultaneously true.
More apropos would be the accounting of Judas's death: Matthew describes him as hanging himself, whereas Acts says he burst open in a field. However this isn't a contradiction either: it may simply be the case that he hung himself in a field, then over time grew bloated and burst open.
As far as I am aware there are no contradictions on the Bible. People often point to the sorts of cases claiming a contradiction, when really it is two authors describing different aspects of a thing that are all simultaneously true.
More apropos would be the accounting of Judas's death: Matthew describes him as hanging himself, whereas Acts says he burst open in a field. However this isn't a contradiction either: it may simply be the case that he hung himself in a field, then over time grew bloated and burst open.