Final answer:
Western European nations were able to establish colonies in Asia and Africa primarily due to their advanced military technology. This allowed for overwhelming military dominance and protection from diseases, facilitating fast and extensive colonial expansion throughout these regions.
Step-by-step explanation:
The characteristic of Western European nations that most enabled them to establish colonies in Asia and Africa was advanced military technology. This superiority in technology included the development of weapons that far surpassed the fighting capabilities of local populations and protection against diseases such as malaria, which had previously been a significant barrier to European expansion in these regions. Consequently, European empires could conquer and control vast territories, spreading their influence and maximizing the extraction of local natural resources.
The swift spread of imperialism by European powers throughout Africa, the Middle East, and Asia was facilitated by their industrial strength and resulting technological advantages, characterized by deadlier weaponry and advancements in healthcare that indigenous societies could not match. The implementation of infrastructure, like roads and telecommunication, by European colonizers further cemented their domination, alongside ideological beliefs in their own cultural superiority and a so-called civilizing mission. These factors, combined with the intense desire to secure raw materials and trade, propelled Western European nations' rapid colonial expansion.