Free trade imperialism is a term that is used to describe the relations between the US and Great Britain on the one hand and the countries of Latin America on the other. In this relationship, the rich countries did not actually colonize the poor countries formally. They left those countries to be politically independent. At the same time, however, they used their economic power to completely dominate those countries.
In the late 1800s, the countries of Latin America were typically trying to modernize and to expand their economies. For example, Mexico, under Porfirio Diaz, needed railroads from its interior to its coasts and to urban centers. The Mexicans lacked the funds and perhaps the expertise to construct such railroads on their own. Therefore, they turned to foreign sources for such funding and expertise. Because the Latin American countries needed funds from the rich world, they were vulnerable to being exploited and dominated. The richer countries came to hold much of the economic power in those nations. They worked together with the rulers of the Latin American countries. Those rulers were enriched and were helped to stay in power. Meanwhile, the rich countries essentially ran the Latin American economies in ways that benefitted the rich countries more than the Latin countries.