Invasions by Barbarian tribes. The most straightforward theory for Western Rome's collapse pins the fall on a string of military losses sustained against outside forces. Rome had tangled with Germanic tribes for centuries, but by the 300's “barbarian” groups like the Goths had encroached beyond the Empire's borders. These are the causes and effects of the falling of the Roman Empire: External military threats were a major cause of Rome's fall, and its effects spread across the empire. ... After Rome was divided, a powerful group known as the Huns began moving west, their numbers growing with captured prisoners and new allies. People from all walks of life were eager to reap the rewards of war.
The 1862 Homestead Act accelerated settlement of U.S. western territory by allowing any American, including freed slaves, to put in a claim for up to 160 free acres of federal land.
Although there are no right answers I'd say the Louisiana Purchase because it gave a huge amount of land and helped with transporting goods across the country. Making it easier to get resources that would otherwise take a long time to transport.
Be sure to change words and parts of my answer otherwise its just plagiarism and you could get an F.