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.
It was such poor territory it wasn't worth the effort of taking it over and having the problems of administration, with insignificant reward.
By conquest.
The Byzantine and Persian empires were weak.
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.
They successively set out to expand and consolidate the Persian Empire.
550 BCE when Cyrus the Great began to establish and expand it to 431 BCE when Alexander the Great took it over as the Macedonian Empire.
Yes, much further. The Roman empire stretched, roughly, from northern Africa to Scotland and from the Atlantic Ocean to the Black Sea.
When it conquered and incorporated the Median Empire in the second half of the 6th Century BCE and was able to use the combined resources to expand to the east and west.
The Greek city-states in Asia Minor revolted against Persian rule. Cities outside the Persian Empire intervened, so the Persians decided to incorporate them within its empire to enforce peace.
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.