Final answer:
The Democratic Republicans favored the Louisiana Purchase of 1803 because of their beliefs in westward expansion, agricultural commerce, and the idea of an agrarian society.
Step-by-step explanation:
The Democratic Republicans favored the Louisiana Purchase of 1803 based on their beliefs in westward expansion, agricultural commerce, and the idea of an agrarian society. Thomas Jefferson, the leader of the Democratic Republican Party and the President at the time, saw the acquisition of the Louisiana Territory as an opportunity to fulfill the vision of an empire of liberty and an agrarian republic. By gaining control of New Orleans and the Mississippi River, Jefferson believed that American farmers would be able to send their produce down the river for trade with European nations, enhancing agricultural commerce.