Question

How did the Roman Republic pay to keep control of these new lands? Thank you everyone for all the help :)

Answer 1

The Romans brought the benefits of Roman civilization and culture to conquered territories,and thus assimilated their populations (at least,those that hadn't been killed or enslaved during the conquest) into the empire as a whole.  

The purpose of this was to win conquered peoples over to the Roman way of life - a higher and more advanced standard of living would reconcile them to Roman rule.  

Sometimes though there would be serious revolts against Roman rule - one in Britain and 2 in Judea were the most serious,so this policy didn't necessarily work everywhere all of the time.

Answer 2

The way that the roman republic pay to keep control of these new lands is : by inflicting high tariff upon its people.
Not only that, they also pay a considerable amount of money to barbarian armies to impose control upon the villages near the borders and the outpost of its enemy.