Final answer:
Macbeth persuades the murderers to kill Banquo by convincing them that Banquo is responsible for their miseries and by questioning their manhood. He suggests that their lives would significantly improve with Banquo's death, thereby inciting them to commit murder.
Step-by-step explanation:
Macbeth convinces the murderers to kill Banquo by manipulating them into believing that Banquo is their enemy and the cause of their misfortune. He plays on their resentment and the human propensity to blame others for personal failures. By suggesting that Banquo is responsible for their unhappiness and lack of success, Macbeth inflames the murderers' desire for revenge.
In Act 3, Scene 1, Macbeth speaks to the murderers, "Are you so gospelled, to pray for this good man and for his issue, whose heavy hand hath bowed you to the grave and beggared yours for ever?" (3.1.88-90). Here, Macbeth is implying that Banquo has been the cause of their ruined lives. He also reinforces their willingness to go to extreme measures by questioning their manhood, "And I will put that business in your bosoms, whose execution takes your enemy off, grapples you to the heart and love of us, Who wear our health but sickly in his life, Which in his death were perfect." (3.1.104-107)