Which of the following best describes how New Mexico and Arizona became part of the United States? ...

Which of the following best describes how New Mexico and Arizona became part of the United States?
 
  A) The United States went to war with Spain in 1821 to gain control of these territories.
  B) American settlement intensified after 1821, which allowed them to buy the entire region from Spain via the Gadsden Purchase.
  C) The United States annexed the Republic of Texas in 1845, which resulted in the Mexican-American War.
  D) The United States cleared out the Native Americans living in the region and settled it before Spain or Mexico could.