Final answer:
Rome's strategy of avoidance, named the Fabian strategy, was initially criticized but eventually led to their victory over Hannibal. The Romans conducted guerrilla warfare that weakened Hannibal's army, who, despite winning battles like Cannae, could not gain significant support in Italy or reinforcements from abroad. The Roman victory at the Battle of Zama ended Hannibal's campaign and secured Rome's dominion.
Step-by-step explanation:
Rome's strategy of avoidance, while initially mocked as a weak approach, ultimately proved to be effective in dealing with the Carthaginian general Hannibal during the Second Punic War. The strategy, championed by the dictator Fabius Maximus and termed the Fabian strategy, involved avoiding large-scale confrontations with Hannibal's forces. Instead, the Romans engaged in guerrilla warfare, continuously harrying Hannibal's army within Italy, which slowly weakened his forces.
Hannibal was a brilliant tactician who achieved several victories against Rome, most notably at the Battle of Cannae in 216 BCE. His army, which included war elephants, terrorized the Roman forces. Despite his battlefield successes, his lack of siege equipment to take Rome itself and his inability to gather support from some of the southern Italian peoples hampered his campaign.
Ultimately, the wear and tear on Hannibal's army from the ongoing Roman harassment, and their inability to reinforce from Spain or Africa due to Roman control of the seas, led to a gradual but continual loss of strength for the Carthaginian forces in Italy. This attrition, combined with Rome's decision to take the fight to Carthage itself, necessitated Hannibal's retreat from Italy to defend his homeland. The decisive Battle of Zama in 202 BCE saw the defeat of Hannibal by the Roman commander Scipio, who earned the nickname 'Scipio Africanus'.
The Roman Senate's policies of dividing and conquering, negotiating from strength, establishing colonies, and transforming former enemies into allies contributed to the robust defense and ultimate victory over Hannibal and Carthage, significantly expanding Rome's territories.