A. The Aztecs welcomed the Spanish with gifts
B. The Spanish took Moctezuma prisoner
D. Smallpox weakened the Aztecs' ability to resist
The statements that contributed to the decline of the Aztec Empire include the Aztecs welcoming the Spanish with gifts, the capture of Moctezuma by the Spanish, and the impact of smallpox on the Aztec population. The desire for gold by Cortés did not lessen and the geographic location of the capital was not a direct factor in the empire's decline. Thus, options A, B, and D are correct answers.
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