Why might the united states have been interested in supporting the new latin american nations in the early 1800s?

To establish a beneficial trade with Latin America and to keep it's country safe.

Explanation:

The United States wanted to establish beneficial trade with Latin America. They wanted Europe to stay out of the affairs of the American continents. The United States promote democracy to create a world free of revolution and war because they wanted to keep their country safe. They needed to keep European countries from creating new republics there. This was the only way that they could stay safe and keep their people safe. They had no option not to get involved.

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it was the "4. potsdam" conference that demanded the unconditional surrender of japan, since it was clear that the japanese would continue to find until the very last man otherwise.