The Mexican Cession started as a feud between America and Mexico when the undisputed land between them and  texas get 16 US soldiers hurt/killed after Texas  joined the U.S.                                               

This lead the U.S. to go to official war with Mexico, This was only two days after President Polk's famous speech. 

We should go to war with Mexico!

In Polk's Speech he talked about how we should go to war with them, in it he talked about how it was all started from the U.S. annexing Texas and why it needed to be ended.

Soon after declaring war upon Mexico they decided to invade it and were meet with forces, then in September 1847 the U.S. captured Mexico City and the war was over.

Mexican land for Money 

In early 1848  Mexico and the U.S. signed the Treaty of Guadalupe Hidalgo where the U.S. bought half their land for 15$ million dollars.

The U.S. then made the Gadsden Purchase for 10$ million in 1853, the land was south of the new land from Mexico and wanted it to use as railroad land since it was very flat and perfect for it.