How might the US purchase of the Louisiana territory from France have helped encourage American settlers to later travel to Oregon and California?

Answer 1

The purchase of the "Louisiana Territory" from France did nothing to help later settlers to California; California was, at that time, part of Spain. However, Oregon was part of the Louisiana Territory (although the border between what would become Washington State and Canada was not yet fixed.) And much of the path that settlers would take to California and Oregon was through the Louisiana Territory.

Perhaps the biggest point was that the purchase of the Louisiana Territory placed the United States adjacent to the Spanish colonies which later became Mexico. In 1835, the Texan war of independence from Mexico began, culminating in the 1836 defeat of the Mexican forces at the Battle of San Jacinto. (The Battle of the Alamo of a few months earlier was a tactical defeat but a strategic victory, delaying the Mexicans and providing time for Texan troops to be gathered.) The acceptance of the Republic of Texas into the United States provoked the Mexican-American War in 1845. The 1846 Bear Flag Rebellion created the short-lived California Republic, and the US crushed the Mexican forces and annexed California.