The Mexican American War~
A war between the U.S. and Mexico spanned the period from spring 1846 to fall 1847. The war was initiated by the United States and resulted in Mexico's defeat and the loss of approximately half of its national territory in the north. In the U.S. the war is termed the Mexican–American War, also known as the Mexican War, the U.S.–Mexican War or the Invasion of Mexico. Which led to...

Outnumbered militarily and with many of its large cities occupied, Mexico could not defend itself; the country was also faced with many internal divisions, including the Caste War of Yucatán. The Treaty of Guadalupe Hidalgo, signed on February 2, 1848, by American diplomat Nicholas Trist and Mexican plenipotentiary representatives Luis G. Cuevas, Bernardo Couto, and Miguel Atristain, ended the war. The treaty gave the U.S. undisputed control of Texas, established the U.S.-Mexican border of the Rio Grande, and ceded to the United States the present-day states of California, Nevada, Utah, New Mexico, most of Arizona and Colorado, and parts of Texas, Oklahoma, Kansas, and Wyoming.

Areas gained by the U.S through the treaty of Guadalupe-Hidalgo colored in white.

Jesus Christ dude...

As per "assimilation" I don't think you understand how long it takes for entire cultures to assimilate, and you still don't have a clear understanding of the word "conquer" apparently if you still want to try to use that word to describe Mexicans living together in a certain area.