Why did the Louisiana Purchase encourage the relocation of Native Americans?

Because American settlers of European ancestry forced the Native Americans out of their lands as they moved west.

Explanation:

The Louisiana Purchase referes to the sale of the French North American territory of Louisiana in 1803. French Emperor Napoleon Bonaparte, facing the Haitian Revolution (1791-1804) and possible war against the United States over Louisiana, chose to settle the matter and sold the territory so he could focus on Europe.

French Louisiana was sparsely populated by French colonists, while Native Americans occupied most of the land. However, American colonists found the newly acquired territories very attractive, and they moved west in large numbers. This led to clashes with the Native Americans who already lived there. In the ensuing decades, the United States government took a carrot and stick approach towards the Native Americans: some tracts of land were bought and paid handsomely, while in other cases, Native Americans were forcefully removed from their ancestral homelands and sent to Indian reservations.