To effectively answer this question, let's first look at how the United States acquired each of these territories. The areas comprising Texas and the Southwest were originally claimed by the Spanish as part of Mexico. In the case of Texas, Mexico encouraged Americans to settle in this largely unpopulated region. Eventually, however, the Americans outnumbered the Mexicans, and they rebelled against Mexican authority. The Texans formed a separate country, the independent Republic of Texas, with Sam Houston as the first president. Their intention was always to become a part of the United States, but this was delayed by Congressional debate over whether Texas would be considered a slave state. Texas officially entered the Union on December 29, 1845.

The Southwest, which included parts of California, Arizona, Nevada, Colorado, Wyoming, and Utah, was ceded to the United States at the end of the Mexican War under the terms of the Treaty of Guadalupe Hidalgo, signed on February 2, 1848. The total area involved was 525,000 square miles, for which the United States paid Mexico 15 million dollars.

Although Spain and Russia had long given up claims to the Oregon Territory, the British and Americans squabbled about the boundaries of the area until the mid-19th century. The Oregon Treaty, signed on June 15, 1846, set the border between the United States and Canada at the 49th parallel, except for Vancouver Island, which the British retained. The portion on the United States side was divided into the Oregon Territory and Washington Territory in 1853.

We can see then that these three territories were all acquired by the United States during the same time period in the mid-19th century, mainly under the presidency of James K. Polk. However, the details of their acquisitions are starkly different. Texas first became an independent country and then joined the Union as a state. The Southwest was bought from Mexico after the Mexican-American War. The boundaries of the Oregon Territory were set with the British by treaty.