Final answer:
The territory became part of the United States through purchase agreements and conquest, such as the Louisiana Purchase and the Mexican Cession.
Step-by-step explanation:
The territory became part of the United States through purchase agreements and conquest.
One significant acquisition was the Louisiana Purchase in 1803, where the United States bought a vast territory from France for $15 million, effectively doubling its size.
Another example is the Mexican Cession in 1848, where the United States gained territories through the Treaty of Guadalupe Hidalgo after winning the Mexican-American War.