How did ancient rome conquer and rule so much territory for such a long time? what were the most important factors in the stability and longevity of rome’s power under the republic and then the empire?

The Roman Empire believed in the saying, "Offense is the best defense", therefore, in order to defend their empire, they saw to it that needed to conquer whatever threats the empire faced. However, the empire grew too large that it could not defend itself anymore, and became vulnerable to attack, leading to its fall.