Why did Hashem tell David to ask?
Rashi: He should pray when he goes to war.
Malbim: From My side, nothing is withheld, if only you will ask. You will be like a son who inherits all his father's property.
Do we find that Hashem promised to give nations to David?
Radak: Yes - "va'Achrisah Es Kol Oyvecha Mipanecha v'Asisi Lecha Shem Gadol k'Shem ha'Gedolim Asher ba'Aretz" (Shmuel II, 7:9). It says "va'Yhi Chol Edom Avadim l'David", "va'Tehi Aram l'David la'Avadim" (Shmuel II, 8:14, 6), "va'Yetzei Shem David b'Chol ha'Aratzos va'Shem Nasan Es Pachdo Al Kol ha'Goyim" (Divrei ha'Yamim I, 14:17).
Is there a difference between Nachalah and Achuzah?
Malbim: Yes. Sometimes one is Nochel (inherits) property overseas, but he is not Ochez (control) them.
What are "Afsei Aretz"?
Radak: They are the ends of the land. Efes is like Ketz (the end). Malbim - David will conquer and control them, just like nearby countries.
