Final answer:
Rival nations used piracy, territorial expansion, and trade competition to undermine Spanish dominance in the Americas.
Step-by-step explanation:
Rival European nations attempted to undermine the dominance of Spain in early American settlements mainly through economic strategies and territorial expansion. The Dutch focused on economically weakening Spanish interests through piracy, and both the Dutch and the French contested Iberian power by establishing colonies in strategic locations like Florida and Brazil that were designed to disrupt Spanish control and trade. Additionally, the Dutch contested Portuguese control more directly by conquering territories in Brazil, while the French and English sought to form their colonies and engage in trade and smuggling activities through companies like the Dutch West Indies Company.