What factors caused european nations to explore the western hemisphere and establish colonies

Fall of Constantinople in 1453. The Turks wanted to impose a tariff on the European cargo ships (something that the Byzantines did not do). Trying to avoid that, the Europeans sailed the other way around, thinking there was just an empty ocean between Europe and Asia. Once they found land, they thought they reached India, but when it became clear that it was a new land, the opportunity to expand empires was there. Of course, there were different motives and strategies to establish them, though not always in the nicest of ways.