As the u. s. expanded west, how were states like texas, california, arizona, and colorado, annexed?

The story of the United States has always been one of westward expansion, beginning along the East Coast and continuing, often by leaps and bounds, until it reached the Pacific—what Theodore Roosevelt described as "the great leap Westward." The acquisition of Hawaii and Alaska, though not usually included in discussions of Americans expanding their nation westward, continued the practices established under the principle of Manifest Destiny.