In "Hamlet", how does the king manage to take advantage of Laertes through their plan?In Act IV, Sene VII
The king uses Laertes' grief over his father's murder to his advantage; he challenges Laertes' 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.
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. Laertes picks up the hint and adds his own idea to the mix: he decides he'll tip the sword with poison. Excellent idea, says Claudius, and just in case THAT doesn't work, I'll poison Hamlet's drink! We're evil geniuses!
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.