European nations expanded their territories by exploiting other parts of the world.
Explain what the effect of this contact was to both life in Europe and life in the Far East and the Americas?
What impact does this expansion have on our world today?
There's no question that the slave trade had a negative effect on the relationship of Europe and Africa, but much less on Europe and Asia. It was the generally superior attitude of the Eurocentric cultures and their economic and social exploitation of the rest of the globe which has caused the most lingering ill effects. The British, for instance, were the most influential in the struggle against slavery, and yet their economic exploitation of every non-European culture they ever encountered did not endear them to anyone. The French were much the same; although not as deeply involved in slavery as Spain or Britain, their blatant exploitation of their possessions in Asia and Africa contrasted with their relatively enlightened actions in North America.
The very concept that the Berlin Conference of 1884-5 divided up Africa among European powers, and with no input from any Africans, shows exactly the arrogance which has led to lingering hatred and fear of Europe and Europeanized nations (US, Australia, etc.) among the "Third World." The Opium Wars between Britain and China, the invasion of Indochina by the French, the actions of France and Britain in the Middle East and the colonization of India are all reasons why the Eurocentric nations are still distrusted by the rest.
The best depiction of this historic trend and its effect on the 20th century is found in Frantz Fanon's classic book The Wretched of the Earth.
There is much to validate this statement. I would suggest that the triangular trade would be the first piece of evidence to substantiate such a notion. The idea of the trade route becoming entirely dependent on the constant and increasing supply of slaves to the West helped foster an idea that other nations were present for their exploitation value. The European nations who participated in the slave trade were responsible for exploiting those portions of the world in order to consolidate political control and maximize economic gain. Additionally, Western nations were able to leverage this power into control, colonization, and control of other nations around the world. This helped to create a twisted perception of the West: On one hand, a level of understandable resentment which is faced with the idea of trying to emulate the power valences that control their lives.