By conquest.
Iran
The Persian Empire was primarily conquered by Alexander the Great in the 4th century BCE. After a series of decisive battles, including the Battle of Granicus, the Battle of Issus, and the Battle of Gaugamela, Alexander defeated the Persian king Darius III. Following Darius's defeat, Alexander continued to expand his empire into Persian territory, ultimately leading to the fall of the Achaemenid dynasty.
He added an area in Central Asia, Thrace and Macedonia.
His persistence in running a 10 year military campaign to take over all the Persian Empire.
He built it by taking over the Babylonian and Lydian Empires, and consolidating these and Persian-Mede territory.
It was such poor territory it wasn't worth the effort of taking it over and having the problems of administration, with insignificant reward.
Iran
Arabia and central Africa.
Persia (modern Iran).
The Byzantine and Persian empires were weak.
By conquest.
The Persian Empire was primarily conquered by Alexander the Great in the 4th century BCE. After a series of decisive battles, including the Battle of Granicus, the Battle of Issus, and the Battle of Gaugamela, Alexander defeated the Persian king Darius III. Following Darius's defeat, Alexander continued to expand his empire into Persian territory, ultimately leading to the fall of the Achaemenid dynasty.
The ambition of the kings to extend their territory and to establish peace, prosparity and security. This extendas the empire from Persia through the Middle East to Libya and Egypt in Africa in the west, and across to today's Pakistan in the east.
The country was too poor to warrant the effort, and it was easier to maintain border security to protect the fertile lands than the cost and effort of occupying the whole territory.
He added an area in Central Asia, Thrace and Macedonia.
Xerxes crossed the Hellespont to invade Greece and expand the Persian Empire.
His persistence in running a 10 year military campaign to take over all the Persian Empire.