How did the louisiana purchase define the united states as nation? a few sentences ?

The Louisiana Purchase almost multiplied the extent of the United States. By any measure, it was one of the huge land exchanges ever, including a region bigger than the present France, Spain, Portugal, Italy, Germany, Holland, Switzerland and the British Isles joined. All or parts of 15 Western states would in the long run be cut from its almost 830,000 square miles, which extended from the Gulf of Mexico to Canada, and from the Mississippi River to the Rocky Mountains. What's more, the cost, $15 million, or around four pennies a section of land, was a stunning deal.

The third one would be the answer