Question

how did america growing and young population spur territorial expansion and how did the united states gain texas and the Oregon country

Answer 1

America was originally only the 13 colonies in the Northeastern United States, but little by little, throughout the 19th century, they were acquiring territories and improving the quality of life, reaching many immigrant families, having greater territories and better life and health, families grew, and the American youth population grew as well.
Texas was acquired after the Texans decided they would not belong to the Mexican government during the Texas War; the state was annexed to the United States on March 1, 1845, being state number 28.
About Oregon, the signing of the Oregon Treaty put an end to the long occupation of Americans and British, who for a long time had disputed the region that includes Oregon, Idaho and Washington, originally inhabited by Amerindian Indians.