ANSWER: Matthew says Judas died by hanging himself. "Then he threw down the pieces of silver in the temple and departed, and went and hanged himself" (Matthew 27:5). However, Luke said Judas burst open. "Now this man purchased a field with the wages of iniquity; and falling headlong, he burst open in the middle and all his entrails gushed out" (Acts 1:1). Is this a contradiction? No.
Isaiah the prophet mentioned an important principle regarding the Bible: "For precept must be upon precept, precept upon precept, line upon line, line upon line, here a little, there a little" (Isaiah 28:10). Jesus said, "The scripture cannot be broken" (John 10:35). The Bible is the inspired Word of God, and we can rely on its trustworthiness. However, it must be rightly divided (II Timothy 2:15).
By putting the two accounts together we get a clearer picture of what happened. Both events are true. But both events did not happen at the same time. Matthew wrote that Judas "hanged himself." Luke explained what happened later: falling headlong, he burst open in the middle and all his entrails gushed out."
We do not have sufficient details to know whether Judas was dead before the fall. Either the hanging was improperly carried out, since it resulted in Judas falling from the noose and bursting asunder on the ground below. Or Judas was dead for some time, and his body decomposed and fell, or slipped from the noose.