What factors contributed to the growth of European empires (1700-1900)?
This is a good question. There are many factors that lead to the growth of European nations from 1700 - 1900. Let me name a few factors.
First, the most important factor by far was the industrial revolution. The industrial revolution started in England and spread to Europe and North America. During this time all work became much more effective. The invention of the steam and combustion engines created a booming economy. Factories were built and Europe began to grow.
Second, along with the growth of technology, there was also growth in education. Indeed, technology and education went together hand in hand.
Finally, there was much overseas exploration during this time. For this reason commodities and resources from other places found their way back to Europe.