Why does the verse say that Yisrael came to Egypt?
Radak: It was due to the famine, to fulfill the decree Bein ha'Besarim "Ki Ger Yihyeh Zar'acha" (Bereishis 15:13).
Malbim: Everything mentioned until now was preparation for this. Shocher Tov gives a parable - they wanted to take a cow to the market, but they could not pull it. They pulled its son, and it ran after its son. So Hashem arranged that Yosef descend, and Yakov came after him.
Why does it switch from "Yisrael" to "Yakov"?
Malbim: Yakov is a lower level than Yisrael. Initially he came to Egypt as Yisrael - an esteemed officer. Afterwards he was a stranger, and is called Yakov - "v'Yakov Gar."
Why does it say "b'Eretz Cham"?
Radak: Mitzrayim was Cham's son.
Malbim: They did not live in the capitol cities, rather, "b'Eretz Cham." This was after Yosef died.
