In "Hamlet" act 4 scenes 7 & 8 how does Claudius manipulate Laertes, an otherwise arguably honourable man, into his plan?
In Act Four, Scene 5, Laertes returns from France and furiously enters the scene ready to kill Claudius. Claudius does an excellent job of settling down Laertes by calmly approaching him, allowing Laertes to voice his grievances, and assuring Laertes that he (Claudius) is not involved in Polonius's murder. Essentially, Claudius earns Laertes's trust by acting calm and allowing Laertes to vent about his father's death. Claudius also assures Laertes that he was not involved in his father's death.
In Act Four, Scene 7, Claudius informs Laertes that Hamlet killed Polonius and explains the numerous reasons why he cannot have Hamlet killed. Claudius then tells Laertes that there is a way he can murder Hamlet without any repercussions. Claudius then brings up the fact that Laertes is a skilled swordsman and says that Hamlet was jealous when he overheard Lamond talking about his skills. Claudius's comments are significant and depict how he manipulates Laertes by complimenting his skills.
Before Claudius elaborates on his plan, he wisely questions Laertes's love for his father and comments that it is imperative for Laertes to act quickly before his passions dissipate. Once again, Claudius manipulates Laertes by playing on his passions and encouraging him to act quickly. Laertes proves his willingness to act by telling Claudius that he is eager to kill Hamlet: "To cut his throat i' th' church" (Shakespeare, 4.7.123). Claudius then explains how he will set up a fencing match between Laertes and Hamlet, and give Laertes a "sword unbated" (one that is not dulled for safety). Laertes decides he will also poison the sword for good measure. Claudius also develops a backup plan to kill Hamlet and tells Laertes that he will also poison Hamlet's drink.
Overall, Claudius manipulates Laertes by fueling his anger, gaining his trust, complimenting his skillset, and assuring Laertes that he will get revenge on the man who killed his father and sister. After Claudius proclaims his innocence in Polonius's death, he directs Laertes's anger toward Hamlet and comes up with a foolproof plan that will allow Laertes to exact revenge.
In two basic ways: he appeals to Laertes' sense of duty and honor in regards to his father, and, he flatters Laertes. He starts by challenging his loyalties to his father: "Was your father dear to you? Or are you like the painting of a sorrow, a face without a heart?...show yourself your father's son in deed more than in words" (ll. 107-109, 126). Claudius is insinuating that if Laertes really loved his father, he would defend his honor in action. This is a sneaky way to get an honorable man to feel that he is being honorable, by defending his father's death. And, Laertes buys into it.
The king also hints around about Laertes' skill with the sword, and that certainly Hamlet would accept a challenge to a duel, where no one would blame Laertes if Hamlet were to "accidentally" die. A duel is an accepted form of competition; it is a noble way to challenge Hamlet, and the king has suggested that Laertes should certainly take Hamlet-of famed skill at the sword-on in a challenge.
So, Claudius plays on Laertes' grief by challenging his loyalty to his father, and his pride by flattering his fencing skills-all to his advantage.