Final answer:
Tensions between Cortés, the Spaniards, and the Aztecs escalated after Cortés took Moctezuma hostage and his men killed Aztec nobles during a religious event, leading to a violent Aztec uprising. The Spanish ultimately conquered Tenochtitlán by allying with local adversaries of the Aztecs and benefitting from the chaos created by smallpox.
Step-by-step explanation:
When Hernán Cortés and his Spanish troops arrived in the Aztec Empire, they were initially welcomed by Emperor Moctezuma II who believed Cortés to be a representative of a potential divine entity. Cortés, aiming to establish power, took Moctezuma hostage and attempted to rule through him, a situation that the Aztecs tolerated for a time. Tensions skyrocketed after Cortés's men massacred Aztec nobles during a religious festival, leading to an uprising in Tenochtitlán, which culminated in the death of Moctezuma and the ignominious retreat of the Spanish. Using local discord to his advantage, Cortés solidified alliances with other native peoples resentful of the Aztecs, such as the Tlaxcalans, and returned to lay siege to Tenochtitlán. After a prolonged battle fueled by internal divisions within the Aztec domains as well as the devastating effects of smallpox introduced by the Europeans, Cortés was able to capture the grand city and claim it for Spain, renaming it Mexico City.