Here are some of the main reasons why European expansion was prevalent from 1450-1750:
1) Increased desire for trade- European countries wanted access to new goods/materials (like spices) that were unavailable in their home countries. In order to obtain these goods easier, they constantly explored for more effective trading routes.
2) Opportunity to become rich- Finding a new resource or new territory would allow a country to prosper financially, as they could sell it to their citizens/other countries.
3) Spread religious views- Europeans wanted to expand their Christian views to other people in different regions and territories.