Final answer:
True. The Republic of Great Colombia was established in 1819 after gaining independence from Spanish rule, encompassing what is now Colombia, Ecuador, Panama, and Venezuela. The claim about the Republic of Texas being established by the Long Expedition is correct, and the Louisiana Purchase doubled the U.S. territory.
Step-by-step explanation:
The Republic of Great Colombia was indeed established in 1819 after the region gained independence from Spanish rule. It encompassed the territories of the modern-day countries of Colombia, Ecuador, Panama, and Venezuela. The existence of the Republic of Great Colombia is a historical fact and was formed to unite the former Spanish colonies in South America under a single government following the independence movements led by Simon Bolivar and others.
This is different from the republics established in North America where, during the Revolutionary War, the individual states opted to create republics rather than monarchies or democracies which is also a historical fact alluding to the nascent American preference for a republican form of government over other forms of rule.
Regarding the Long Expedition, it established a short-lived republic in Texas known as the Republic of Texas. Pennsylvania's constitution during the Revolutionary Era was one of the most liberal, not conservative, giving a false statement to the claim of it being the most conservative. The Louisiana Purchase indeed doubled the territory of the United States, thus supporting the expansion and formation of new territories and states within the burgeoning nation.