Final answer:
The Portuguese aimed to establish trade routes, secure resources like gold and spices, and enhance their maritime control in eastern Africa, creating trading posts and forts for economic gain and strategic advantage.
Step-by-step explanation:
The Portuguese government's goals for returning to the eastern African coast during the 15th and 16th centuries predominantly revolved around establishing trade routes, securing valuable resources such as gold and ivory, and expanding their maritime control to further their economic interests.
They established trading posts along the coast of West Africa, where they engaged in the trade of gold and later slaves, setting up fortresses known as feitorias to support their activities. Additionally, Portugal sought to control the spice trade by finding a sea route to Asia, driven by the desire to weaken Muslim trade dominance and enrich the Christian world.