In the late 1800s, how did european countries build empires

by settling newly discovered lands  

Explanation:

By the mid-1800s, population and economic growth in several European countries had led to a new type of colonization of newly discovered land, which had the character of domination (and sometimes extermination) of peoples occupying distant territories and their natural resources, creating great colonial empires. One of the most important aspects of this colonization was slavery, with the "export" of a large part of the African population to the Americas, with dire consequences both for the Black Continent and for the descendants of slaves,

hawaii was the final state