Answer:
He hopes asking for it will cause Perseus to leave his mother behind.
Step-by-step explanation:
King Polydectes asks Perseus to bring him the head of Medusa because "he hopes to ask for it will cause Perseus to leave his mother behind."
This is evident in the fact that King Polydectes believed that Perseus would leave his mother (Danae) behind, and later die in his pursuit of getting the head of Medusa. Thereby, he would be able to have the perfect opportunity to marry Danae without interference.