The entire states of California, Nevada, Utah, most of Colorado, most of Arizona and almost all of New Mexico were taken from the Mexicans in the war that started in 1845. Texas we got by annexing it 10 years after Anglo settlers declared independence from Mexico in 1835. We didnt pay them for any of this.
Not strictly true:
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 and gave the U.S. undisputed control of Texas, established the U.S.-Mexican border of the Rio Grande River, and ceded to the United States the present-day states of California, Nevada, Utah, and parts of Colorado, Arizona, Oklahoma, New Mexico, and Wyoming. In return Mexico received US $18,250,000 ($457,373,077 today)—less than half the amount the U.S. had attempted to offer Mexico for the land before the opening of hostilities—and the U.S. agreed to assume $3.25-million ($81,450,000 today) in debts that the Mexican government owed to U.S. citizens
(ref: Mexican-American War
(Wikipedia). We may have given Mexico little choice in the matter, but she was
paid for that land.
As for Texas: Texans declared and fought for independence from Mexico on their own. It was only after she'd been an independent republic for nine years that she was annexed by the U.S., at her invitation.