The correct answer to this open question is the following.
Unfortunately, you did not include the name of the imperialist nations neither the regions that you selected. Without that information, we cannot properly answer your question.
However, trying to help you, we can answer in the following general terms.
Let's put the example of Great Britain.
The imperialistic interests of the British Crown in -for instance- Africa were basically economic and political. But above all, economic.
European superpowers knew that African nations lived in places rich in natural resources. So these European countries were only interested in exploiting the many raw materials ad natural resources of the African regions.
That is why European countries such as Great Britain, France, Germany, Portugal, and Spain participated in the so-called "Scramble for Africa."