Compare and contrast the acquistion of Texas and the Southwest with that of Oregon.
There are more differences between these two acquisitions than there are similarities.
The only real similarity between these two is that both places were, originally, taken by Europeans from the Native Americans. In both places, there were still Native Americans that had to be "removed" or "pacified" after the US acquired the new territory.
There is a significant difference in how the US acquired each area, though. The US acquired Texas and the Southwest through coercion. Mexico did not recognize Texas's independence when the US annexed Texas and it took the Mexican-American War to get the rest of the Southwest for the US. By contrast, the US got the Oregon Territory peacefully. The US got Oregon by making a treaty with Great Britain. There was no coercion involved.
So, the similarity is that both areas were originally taken by force from Native Americans. However, the US took the Southwest by force from Mexico but got Oregon peacefully from Great Britain.