An example of a purchase would be the Louisiana Purchase of 1803. Here, Thomas Jefferson bought the entire Louisiana territory from France for approximately 13 cents an acre. America nearly doubled in size with this purchase. The reason Thomas Jefferson felt so compelled to purchase the land and not to engage in war was because the other countries showed no sign of provoking war and this would solve the problem of the closing of the New Orleans port in a peaceful way.
Negotiating was a very effective and peaceful was of settling conflicts. Negotiations was used the Oregon territory conflict with Britain and Spain. First, the Adams-Onis treaty of 1819 stated that Spain would leave Oregon. This was a huge step for America in gaining control of the Oregon territory. The next obstacle were the British. It was not for a long time until America has complete control over Oregon. Before that, America shared joint occupancy with Great Britain in Oregon. This was easily settled by negotiations with the British and Spain.
The United States did not always have the great fortune to settle things peacefully. Sometimes the U.S. had the use violent methods to get what they wanted. An example of this would be the Trail of Tears in Georgia. In the