In what ways did the united states acquire western lands?

"The religious fervor spawned by the Second Great Awakening created another incentive for the drive west. Indeed, many settlers believed that God himself blessed the growth of the American nation. The Native Americans were considered heathens. By Christianizing the tribes, American missionaries believed they could save souls..."

Or

Louisiana Purchase, 1803
Mexican cession 1849
and also, although not in the west, the annexation of Florida 1819

The answer would be advertising.