Final answer:
The terms used to criticize President Roosevelt's hardball style of dealing with foreign countries are the Roosevelt Corollary and Big Stick Diplomacy.
Step-by-step explanation:
One term that is used to criticize President Roosevelt's hardball style of dealing with foreign countries is "Roosevelt Corollary".
The Roosevelt Corollary was an extension of the Monroe Doctrine, which stated that the United States would intervene in Latin American affairs to protect US interests. Critics argued that this aggressive approach to foreign policy was imperialistic and undermined the sovereignty of other nations.
Another term often used to describe Roosevelt's approach is "Big Stick Diplomacy", which emphasized the use of military force and the assertion of American power to ensure favorable outcomes in international negotiations.