California, Nevada, Utah, and most of Arizona and New Mexico, plus a bit of Colorado and Wyoming, were part of the forced sale known as the Mexican Cession, in the 1848 treaty ending the Mexican War, but the Gadsden Purchase of 1853 was voluntary—the Mexicans have no claim on that territory. Giving them back the land north of the Gadsden Purchase would make for a pretty strange border. Tucson would still belong to the US, but Flagstaff would be Mexican.
Definition: Area of the present-day United States that Mexico agreed to give up as part of the Treaty of Guadalupe Hidalgo, which ended the Mexican-American War. This territory included all of the present-day states of California, Nevada, and Utah and also parts of Arizona, Colorado, New Mexico, Utah, and Wyoming.
