Correct the one error its the law

What is the name for the main idea behind the settling of western lands by americans in the early-1800s?

Which expression is equivalent to (fg)(5)

1. discovered the new world balboa 2. explored the north american southwest hudson 3. his crew was the first to sail around the world vespucci 4. conquered the incas of peru cortes 5. discovered the pacific ocean columbus 6. conquered the aztecs of mexico cabot 7. discovered fishing grounds off newfoundland pizarro 8. looted spanish vessels for england drake 9. claimed the hudson river area for dutch coronado 10. priest who explored the mississippi marquette 11. man for whom the new world is named magellan