Contradiction clarified: Judas' death

In Matthew 27:5 Matthew says that Judas after betraying Jesus returned the money to the Jews who did not accept it because it was stained with blood. Then he threw back the money and then went and hanged himself.

In Acts 1, Apostle Peter says that Judas actually bought a field with the money and then fell and had a burst abdomen and this was his end.

Clarifications:

Approach 1: Harmonization 
Mathew and Luke are using a literary technique called "telescoping" or "compression".
They are not divulging all information about the issue. Matthew states the hanging part whereas Luke is stating the body falling and abdomen bursting.

Mathew states the fact that Judas threw the money which was not accepted by the Jewish leaders when he returned. Luke talks about Judas acquiring a field with the money and when his hung body falls with the resulting burst abdomen.

Approach 2: Typological 
According to this view, Matthew is portraying Judas in the light of Ahithophel in the Old Testament who was a traitor and betrayer. Since Mathew's gospel is filled with typos, it cannot be dismissed easily and should be seriously considered as an explanation.

"However, I would now opt for the idea that this is an example of Matthew's creative use of an OT "type". This would combine the idea that Matthew is not actually describing Judas' death, with Matthew's use of the OT texts as typologies.

Audrey Conrad, in "The Fate of Judas" (Toronto Journal of Theology [7] 1992), notes that Matthew's unique words "departed" and "hanged himself" are found in combination in another place in the LXX:

2 Samuel 17:23 And when Ahithophel saw that his counsel was not followed, he saddled his ass, and arose, and gat him home to his house, to his city, and put his household in order, and hanged himself, and died, and was buried in the sepulchre of his father.

Conrad notes that rabbinic interpretation of Ps. 41:9 ("Yea, mine own familiar friend, in whom I trusted, which did eat of my bread, hath lifted up his heel against me.") thought that Ahithophel was the traitor David was describing -- and of course this same verse was applied by Jesus to Judas (John 13:18).

Conrad still thinks there are not enough parallels (!) but we would maintain that the parallels are sufficient, and that Matthew is indeed alluding to the traitor Ahithophel in this passage, and is therefore NOT telling us that Judas indeed hanged himself, but that Judas fulfilled the "type" of Ahithophel by being a traitor who responded with grief and then died. Matthew is thereby making no statement at all about Judas' mode of death, and Luke's "swelling up" stands alone as a specific description of what happened."     

                    ------------------  http://tektonics.org/gk/judasdeath.php

Approach 3: Information selection by Audience

Matthew was writing to Jewish audience and Luke to gentile audience.

"Matthew was writing to the Jews, who believed that someone was under the judgment of God by hanging from a tree. Deuteronomy states, “He who is hanged is accursed of God” (Deut. 21:23). By contrast, Luke was writing to the Gentiles, who believed that suicide was honorable, so he chose the imagery of a decomposed, unburied body for Judas, which (to a Gentile) would communicate the curse of God. Both accounts were accurately telling the story, but they emphasized different portions of the story to communicate to their respective audiences."  

                                      ------------------------------  http://www.evidenceunseen.com/bible-difficulties-2/nt-difficulties/john-acts/acts-118-how-did-judas-die/

Conclusion:

A Combination of Approach 1 and 3 or 2 and 3 is a good way to resolve this apparent contradiction.