Why did Eurasia conquer America, Africa, and Australia?

Europe and Asia's intent to conquer the Americas, Africa, and Australia grew out of two primary drives. The first was a pervasive religious imperialism founded on the Christian doctrine to spread "God's mission." This drive was most prominent in Europe, while Asia was motivated by its own brand of imperialism based on more secular and dynastic values. Both of these imperialist brands utilized appeals to higher powers (God, or rich national legacies) to morally justify starting physical and ideological warfare that decimated the native cultures of the Americas, Africa, and Australia.
The second drive was arguably an economic imperative to seize the means of production in new and unexploited regions of the world. Most political leaders during the era of colonialism were afraid of what lay on the frontiers of the known world, and fixated on conquering them by gouging out their resources and laying them bare and innocuous. After destroying countless indigenous cultures and incorporating their people into the fledgling slave trade, Europe and, to a lesser extent, Asia, sought to project their values onto the new world and mould it into their ideal self-images.