Why was Hannibal defeated in the war with the Romans, despite a brilliant victory at the Battle of Cannes?

Because Hannibal did not know how to use victories to his advantage. Thus, even such a great victory as the battle of Cannes did not become decisive in the war. At the same time, the Romans were able to immediately use the first major victory over Carthage, after the Battle of Zama, where Hannibal’s troops were defeated. So Carthage was forced to recognize the victory of Rome in this war.