Final answer:
The Persian Empire expanded through conquest and assimilation of neighboring territories. Cyrus led the Persians to conquer the Medes and embarked on a campaign of conquest that lasted twenty years. While they controlled a vast territory, their attempt to expand into mainland Greece was unsuccessful.
Step-by-step explanation:
The Persian Empire expanded by conquering neighboring territories and assimilating their people and military into the empire. One of the key leaders in this expansion was Cyrus, who conquered the Medes and embarked on a campaign of conquest that lasted twenty years. The Persians controlled a vast territory stretching from central Asia and Afghanistan to Asia Minor, Egypt, Libya, and Macedonia. However, their attempt to expand further into mainland Greece was ultimately defeated.