Since I'm a theology major i don't take religious discussions lightly.
The whole idea of a Muslim being a violent extremists should be a contradiction. If you are a so called peaceful Muslim and then go and practice any types of violence then you are no longer a Muslim but a terrorist and bring shame to Islam if they are of peace.
Same with Christianity, God's words say that if any acts of violence are committed and claim to be in his name, then they are not of God, and God is not in them.Violence is frowned upon in many religions, but it seems Muslims practice it the most. It just seems the true Muslims are following Mohammad's path.
It seems it's OK for Muslims to commit violence as long as its in the name of "Allah". Mohammed himself was not a peacemaker, and used violence in many occasions for persuasion. If you claim to be a Muslim and are not following Mohammed, then that would make you a non-Muslim and a perpetrator of his teachings.