What is the meaning of "v'Chagosem"?
Chagigah 10b: It means (not 'celebrate,' but rather) 'bring a Korban Chagigah.' We learn this via a double Gezerah Shavah - from "v'Yachogu Li ba'Midbar" (Shemos 5:1), and from the Pasuk "ha'Zevachim u'Minchah Higashtem Li ba'Midbar?" (Amos 5:25). 1
See Torah Temimah, citing Chagigah (loc. cit.), and note 2 to Shemos 5:1.
When does the Mitzvah of "v'Chagosem" apply?
Rashi: It applies on the same day that we commemorate - the day that we left Egypt. 1
Rashi: I.e., the day after the Korban was eaten in Egypt (the night of the fifteenth), as the Pasuk writes in Bamidbar 33:3. Refer also to 13:3:1:2.
Why does the Torah add the word "La'Shem"?
Beitzah 19a: To teach us that, even though on Yom Tov, one may basically only slaughter for Ochel Nefesh - what is for one's own consumption; one is permitted (obligated) to bring Shalmei Chagigah and Shalmei Simchah, as well as Olos Re'iyah, which are mainly for the sake of Hashem. 1
See Torah Temimah, note 111.
Having said "l'Doroseichem," why does the Torah add "Chukas Olam"?
Rashi: Because we would otherwise have thought that the Mitzvah is restricted to two generations. 1
Pesikta Zutresa: To include the days of Mashi'ach. 2
Oznayim la'Torah: To teach us the obligation to celebrate Pesach even when we are in Galus, referring to it as a Chok because celebrating our freedom when we are in Galus seems illogical. 3
See Sifsei Chachamim and Torah Temimah, note 112.
Moshav Zekenim: But all the Mo'adim will be Batel in the future, except for Yom Kipur and Purim! That is after Techiyas ha'Mesim in the days of Mashi'ach ben David. Here we include in the days of Mashi'ach ben Yosef.
Oznayim la'Torah: And the underlying reason for this is because our freedom from Egypt was predominantly a freedom of the soul, from the Avodah Zarah of Egypt - a freedom that lasts forever and that applies at all times, even during Galus Bavel and Galus Edom.
QUESTIONS ON RASHI
Rashi writes: "As a remembrance - for generations." What is Rashi telling us, and what is his source?
Gur Aryeh: This Pasuk is not teaching us to remember [the day of the Exodus] constantly; but rather every year for all generations. 1 This is clarified by the Pasuk's conclusion, "[For all your generations, as] an eternal statute you shall celebrate it."
We do learn from another verse that we must remember the Exodus daily - "In order that you remember the day of your leaving Egypt, all the days of your life" (Devarim 16:3).
Rashi writes: "L'Doroseichem - I might think for a minimum two generations; so the verse says '... as an eternal statute you shall celebrate it.'" What then do we learn from the word "l'Doroseichem"?
Gur Aryeh: It clarifies that this Pasuk does not teach us to remember it constantly; but rather for all generations. See above (12:14:0.01:1). 1
Thus, Gur Aryeh shows how both terms, "l'Doroseichem" and "Chukas Olam" are necessary.
