Act IV scene 7 is a classic Shakesperian scene of manipulation and persuasion as Claudius meets with Laertes and convinces him to kill Hamlet. It is well worth revisiting this scene and examining it closely because here we see how Claudius persuades Laertes to kill Hamlet for him.
One of the key elements of this scene to me is when Claudius mocks Laertes to spur him on in anger to revenge against Hamlet. Note how Claudius says to Laertes:
Laertes was your father dear to you?
Or are you like the painting of a sorrow,
A face without a heart?
Claudius is deliberately angering Laertes to manipulate his emotions. By questioning the sincerity of his love he goads Laertes into a rash revenge plot - completely unlike Hamlet, of course, for Laertes does not hesitate at all in achieving his goal of revenge. Note how Claudius goes on to challenge Laertes following this insulting question:
What would you undertake,
To show yourself your father's son indeed,
More than in words?
The challenge is clear - if you do love your father, show it but not in words. What are you prepared to do?
So is hatched the final revenge plan that brings death to both Laertes and Claudius. I have highlighted some of the examples you will want to think about but it is well worth considering the scene as a whole to pick up more examples of persuasive language. Claudius shows himself in this scene to be a canny manipulator of people, as Laertes himself discovers just before he dies.