Final answer:
While Hernán Cortés dealt with a threat from Diego Velázquez on the coast, Pedro de Alvarado faced a rebellion in Tenochtitlán. The Spaniards eventually overcame the Aztecs, aided by military technology, smallpox, and alliances with native groups.
Step-by-step explanation:
While Hernán Cortés went down to the coast to confront the soldiers sent by Diego Velázquez, his lieutenant Pedro de Alvarado and the remaining Spaniards faced rebellion within Tenochtitlán. Cortés had initially been welcomed by the Aztecs, partly due to their belief that he was the god Quetzalcoatl, and he proceeded to take the Emperor Moctezuma hostage. However, this uneasy peace did not last, and in Cortés's absence, Alvarado, fearing an uprising, ordered a massacre during a festival, which further inflamed tensions, leading to an Aztec rebellion. When Cortés returned, he found the city in chaos and, on a night that became known as Noche Triste, he and his men had to flee, suffering heavy casualties. Nevertheless, with reinforcements and the help of native allies, particularly the Tlaxcalans who opposed Aztec rule, Cortés laid siege to and eventually destroyed Tenochtitlán, claiming the land for Spain and establishing Mexico City over its ruins. In 1522, Cortés was appointed governor of the newly christened New Spain.
Success was not solely due to Spanish military prowess; factors such as the alliances with various native groups, the introduction of smallpox, and the technological advantage of Spanish weaponry played significant roles. The conflict culminated in the siege of Tenochtitlán and the fall of the Aztec Empire.