Final answer:
The U.S. chose to pay for the western territories of Mexico due to concerns over managing a large, diverse population and the costs involved, as well as the desire to avoid further complicating the issue of slavery within U.S. politics.
Step-by-step explanation:
The U.S. agreed to pay Mexico for the western lands following the Mexican-American War for multiple reasons.
One significant factor was the issue of racism; many Americans considered the Mexican people to be of lower status and preferred to populate the newly acquired territories with Caucasian settlers.
Additionally, managing an entire country with a turbulent history and a large population of mixed ancestry would have been a complex and costly endeavor for the U.S.
The Treaty of Guadalupe Hidalgo reflected a more pragmatic approach, increasing U.S. land mass by 20% and gaining crucial ports for trade with Asia.
The Manifest Destiny mindset certainly pushed for expansion, yet the U.S. opted for a manageable cession rather than taking over all of Mexico.
This decision was also influenced by the potential complications related to the issue of slavery and the political balance within the United States.