Why does the Torah insert the word "Kol Mikn'cha Tizachar"?
Bechoros, 3a: To teach us that the entire animal must belong to a Yisrael - to preclude an animal that one owns in partnership with a Nochri from the Din Bechorah. 1
With reference to ythe mother. See Torah Temimah, note 23.
Why does the Torah insert the Mitzvah of B'chor here?
Rashbam: Because, it was as a result of Makas Bechoros 1 that the firstborn were sanctified.
Seforno: Refer to 3:18:2:1.
Oznayim la'Torah: To avoid serving Avodah Zarah, it is not sufficient merely to keep one's distance from its worshippers. One must also remember the day that one left Egypt - Who took us out and why. Consequently, we need to recall a. how, when we left Egypt, the dough did not manage to rise before the King of Kings, Hakadosh-Baruch-Hu revealed Himself to us and redeemed us; b. to sanctify the firsborn - to remember the miracle of Makas Bechoros, and c. to bring the Korban Pesach - to remember how Hashem "plagued the Egyptians and saved our houses". In that way, we will never again declare to a golden calf 'Eileh Elohecha Yisrael asher He'euche me'Eretz Mitzrayim!' 2