gex gex - For everything you’d ever want to know about the Mexican war, read through The Aztec Club of 1847.
As for how America would look:
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For starters, most of the U.S. territory acquired from Mexico would have remained part of Mexico.
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However, it’s fairly likely that Cortina in Tejas and Vallejo in California would have pressed on with independence movements. The Republic of the Rio Grande and the Republic of California would then border the south and west U.S., respectively.
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Having lost the war, demoralized Polk would have lost part of the Oregon territory to Canada.
I’ll let you reach your own conclusions about how all that would have affected the U.S. Civil War, the Indian Wars and Brigham Young.