Final answer:
The Romans used techniques such as divide and conquer, negotiation from strength, establishing colonies, building roads, and transforming enemies into allies to administer their acquired foreign provinces.
Step-by-step explanation:
The Romans used a variety of techniques to administer the foreign provinces they acquired. Firstly, they would attempt to divide and conquer by defeating one enemy at a time and turning enemies against each other. They also negotiated from a position of strength, continuing wars until winning major engagements to negotiate for peace. To secure conquered lands, they established colonies as a first line of defense and built well-constructed roads for quick military response. They transformed former enemies into allies, granting Roman citizenship to local elites who supported Rome.