Q: How was the growth of the republic aided by the Roman army's use of legions in warfare?
A: Well, for starters the Roman Army was considered the absolute most advanced of its time. They created the Roman Empire. (What is the Roman Empire you may ask? Well its quite simple... Indeed, the Roman Empire is a gigantic part of Western Europe.) Also, Rome itself was greatly benefited from the riches that the Roman army had brought back from all of their conquered territories.
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Hope this helped :)