How does Macbeth convince the murderers that they should kill Banquo and Fleance in Act Three Scene 1 of Macbeth?
Macbeth at this point in the play has lost all of his previous uncertainty related to pursuing his bloodthirsty ambitions. The witches' prophecies had proved correct for his ascension to be Thane of Cawdor, and now through submitting to the temptation to murder Duncan he has become king of Scotland. He is now looking to hire three (unnamed in the play) murderers to do his dirty work of depriving Banquo and his descendants of fulfilling the witches' prophecy of taking the throne. Macbeth's ambitions and lust for power now know no boundaries.
Macbeth convinces the murderers that all their problems in life and the general poverty they live in are not his fault but Banquo's. He therefore urges them on to take revenge for this state of affairs. It is not made clear in the play what exactly either Macbeth or Banquo ever did to cause the murderers hardship in the first place.
Macbeth also challenges the men's masculinity as a spur to action (masculinity is a recurring motif in the play - we see Macbeth's masculinity challenged by Lady Macbeth for example). He does this through the analogy of breeds of dogs, challenging the men to prove themselves as a stronger breed of man, just as there are stronger breeds of dogs - "...And so of men. Now, if you have a station in the file, Not i' th' worst rank of manhood, say 't, And I will put that business in your bosoms..." (Act 3 Scene 1 lines 103-106).
Macbeth therefore uses a two pronged strategy to manipulate the men into fulfilling his own evil purposes.