Question

how might a belief in social darwinism and a desire for national survival motivate countries to dominate other countries or regions

Answer 1

Because they feel like they must take out other countries before they get taken out (survival of the fittest)

Answer 2

A belief in social Darwinism and a desire for national survival was justified by the idea of "Survival of the fittest" from Charles Darwin. Some Social Darwinism followers thought that applied to society, white Anglo-Saxon were a superior race.

Social Darwinism and a desire for national survival motivate countries to dominate other countries or regions justified imperialism by taking over under-developed colonies that were not modern with the purpose to help them with decisions and actions to modernize its society.

Imperialism is a consequence of considering the idea of "Survival of the fittest". A strong nation wants to take control of another weak to impose its dominion