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 Who: United States, President James Polk, General Taylor, Col. Kearney, Commodore Stockton and others vs. Mexico, General Santa Anna

What: Dispute about the border, whether or not Texas could be part of the USA, and belief of many US citizens that there was a "manifest destiny" that the country extended all the way from the Atlantic Ocean to the Pacific Ocean and include Texas, California, and the territory in between that had been part of Mexico.

When: April 1846 to  February 1848

Where: War began at Coahuila, near the Rio Grande River. Included battles at Monterey, Buena Vista, Vera Cruz, Puebla and other places. Ended at the  Battle of Chapultepec in Mexico City. Treaty of Guadalupe Hidalgo ended the war.

How: The USA had superior weapons, especially artillery and cannons. The Mexican government was disorganized, not prepared for war. Mexican troops suffered disease, fatigue, and desertion. When the US won, Mexico gave up the disputed territory extending from Texas to California and the USA paid 15 million dollars to Mexico for the territory.

Explanation:

no one really purchased it themselves, it was all america, they had debates etc.

to force terrorists groups to stop attacking western targets using massive military force.