Cyrene.
No one expended the Greek empire because there was not a Greek empire. Alexander the Great, the king of Macedon, with allied Greek city-states conquered the Persian Empire. After his death his generals fought each other. This resulted in the division of Alexander's conquests into the Kingdom of Pergamon, the Seleucid Empire and the Ptolemaic Kingdom.
United Empire: Rome Western Empire: Rome then Ravenna Eastern Empire: Constantinople
There was no Roman empire in 753 BC. That is the traditional date of the founding of the city of Rome. It was not until roughly 200 years later that the little city-state grew into an empire.
culture of the eastern roman empire survived the fall of by still being used by the byzantine empire (but i cannot give specific culture dtails)
The city of Jerusalem was within the Persian Empire.
Which city are you asking about. There were hundreds of cities within the Persian Empire.
baghadad
The Persian Empire versus coalitions of Greek city-states led first by Sparta, then by Athens.
The ancient Persian empire was located where Iran is today. Babylon was its capital city.
The Persian Empire and a coalition of Greek city-states.
The Persian Empire versus varying combinations of Greek city-states.
The Greek city-states occupied by, or threatened by, expansion of the Persian Empire in the eastern Mediterranean littoral.
The Persian Empire and various combinations of Greek city-states.
The Persian Empire and the eastern Greek city-states.
Memphis
Persepolis.