Seeing as the Pasuk in Re'eh (Devarim 16:4) prohibits keeping Chametz 'in all your borders' (also including fields and vineyards - see Sifsei Chachamim), why does the Torah write here, "in your houses"?
Rashi: To teach us that the prohibition against retaining Chametz on Pesach is confined to one's own Chametz, but does not extend to the Chametz of a Nochri that is lying in one's house and on which one did not take any responsibility. 1
Ramban: It comes to exclude the Chametz of a Yisrael that one has deposited in the domain of a Nochri from 'Bal Yera'eh' and 'Bal Yimatzei.' 2
Pesachim 5a: It teaches us that "in your houses," as 'in all your borders,' one is not liable for Chametz belonging to a Nochri or to Hekdesh. 3
What is the definition of "Machmetzes"?
Pesachim 43a: It is Chametz that came about (not from itself, but) due to something else (such as sourdough).
Rashi (to 12:19 and 12:20): It is the sourdough itself. 1
Refer to 12:19:2.1:1 and its note.
Why does the Torah add this verse, "Ki Kol Ochel Machmetzes, [v'Nichresah, etc.]"? We already know that the penalty of Kareis applies, from verse 12:15?
Rashi: This verse incorporates Se'or (sourdough) in the penalty of Kareis - which we would not have known from Chametz, since, as opposed to Chametz, it is not edible. 1
Rashi: And had the Torah not written Kareis by Chametz, we would not have learnt it from Se'or, since, as opposed to Se'or, Chametz does not cause other dough to rise. See Torah Temimah, note 174.
What Halachos do we derive from what the Torah writes here, "Se'or Lo Yimatzei b'Vateichem;" and later, "v'Lo Yera'eh Lecha Se'or b'Chol Gevulecha" (13:7)?
Pesachim 5b: The word "Lecha" teaches us that it is only one's own Se'or (and Chametz) that one is forbidden to retain, but not that of Hekdesh or of a Nochri. 1
Pesachim 8b: The latter Pasuk comes to incorporate Chametz that is not in the house, but rather in pits, trenches or caves, in the Isur of "Lo Yimatzei."
The current Pasuk teaches the Lav of Bal Yimatzei; and the latter Pasuk, that of Bal Yera'eh.
Torah Temimah: Whereas from here we learn that one is only permitted to retain the Chametz of a Nochri if one did not accept responsibility - as implied by the Lashon "Lo Yimatzei - Pesachim (loc. cit). This will be discussed further in 13:7.
Bearing in mind that a Ger is Chayav in all the Mitzvos like a Yisrael, why does the Torah need to include "Ger" in the Mitzvah of eating Matzos?
Rashi: Since the miracle of the Exodus was confined to Yisrael, we would otherwise have exempted him from commemorating it. 1
Refer to 12:48:1.1:1 as to why they are included.
How much Chametz must one eat to be punishable?
Moshav Zekenim: One is only Chayav Kareis for eating a k'Zayis, but Malkos for any amount; unlike other Isurim, for which one is Chayav Malkos only for a k'Zayis. 1
Moshav Zekenim: Even though Mashehu is forbidden, it is Batel in sixty parts [of Heter], like other Isurim - Min b'she'Eino Mino. Min b'Mino is Asur b'Mashehu (Pesachim 29b) (PF).
QUESTIONS ON RASHI
Rashi writes: "[Se'or] shall not be found in your homes - ... Just as your house is in your Reshus (domain), so too, [the verse that prohibits Chametz] 'in your borders' (13:7) [refers only to within] your domain; this excludes a Nochri's Chametz that is by a Jew, and he did not accept responsibility for it," (i.e., in such a case the Chametz need not be removed). Ramban asks - How can the words "in your homes" exclude that case? After all - the Chametz is in the Jew's home!
Ramban: [Unlike Rashi,] our verse is coming to exclude the inverse case - Chametz belonging to a Jew, that is in a non-Jew's house. (Rashi's case is also exempt from Bi'ur - but based on a different Pasuk, "v'Lo Yera'eh" (13:7). 1 )
Mizrachi: What does our verse, "in your homes" add, that is not covered by "in all your borders" (13:7)? Rather, "homes" is not literal; it means '[Chametz in] your control and domain.' Thus, it comes to exclude Chametz belonging to a Nochri, for which the Yisrael accepted no responsibility - which is surely not under his control. 2
Gur Aryeh: "In your homes" excludes Chametz of a Jew by a Nochri's home. 3 "Your Chametz shall not be seen, etc." (13:7) excludes Chametz of a Nochri by a Jew's home, which he cannot destroy.
Ramban: There cannot be a Lav transgressed if the Chametz is in a Nochri's home - as the Pasuk says "in your homes"! The Ramban adds that mid'Rabanan, however, it is forbidden.
Gur Aryeh initially explains Rashi this way as well.
"Home" is taken literally; this explanation parallels the Ramban. Gur Aryeh explains how this explanation also conforms with the Mechilta, and with Gemara Pesachim 5b.
Rashi writes: "For anyone who eats Machmetzes, etc. - [This verse] teaches the Kareis punishment for [one who eats] Se'or (sourdough)." How does the term "Machmetzes" imply Se'or?
Gur Aryeh: The term "Machmetzes" implies something that has the ability to turn other things into Chametz. 1
I.e., we should understand "Machmetzes" not as a noun, but rather as a verb in the causative (something that is Machmitz Acherim). (One could ask that grammatically, the term "Machmetzes" indeed seems to be a noun - 'the object that results from the process of Chimutz.' Parallel words include "Machteres" (22:1) - a tunnel, the result of digging (Chatirah); and "Machberes" (26:4) - a set [of curtains], the result of joining (Chibur). And indeed, the Gemara (Pesachim 28b and 43a) interprets "Machmetzes" that way as well, "Nis'chametz Machamas Davar Acher" - Chametz that came about through some leavening agent - CS.)
Rashi writes: "'Among [both] converts (Ger) and citizens of the Land (Ezrach)' - Because the miracles happened to Yisrael, it was necessary to include the converts." Seemingly, the fact that the term "Ezrach" would exclude Gerim, is sufficient reason to include them in their own right. Why does Rashi need to add the reason, that they were not present at the miracles of Exodus?
Gur Aryeh (to 12:49): Indeed, what Rashi means is that since some exclusion is implied by "Ezrach," we would choose to exclude converts before any other group - because they did not experience the miracles of the Exodus. That is why the Torah must include them specifically. 1
But now that Gerim are explicitly included in these Mitzvos, the term "Ezrach" must be coming to exclude something else. Refer to 12:49:1.2:1.
