How do you think the aztecs were able to establish an extensive empire in such a relatively short period of time?

The Aztecs were able to amass such a large empire in such a short period of time because the groundwork was already there! As the Aztecs began to amass power, city-states and other domains already existed in Central Mexico. Therefore, the Aztecs (who in their early history were renowned mercenaries) eventually began to conquer these other locations and bring them under Aztec control. So instead of having to go out an build an extensive empire, the Aztecs were able to conquer smaller political entities that already existed.