"Kol Petter Rechem Li". What are the connotations of Petter Rechem"?
Rashi: As in Mishlei 17:14 "Poter Mayim Reishis Madon".
What are the connotations of "Tizachar"?
Rashi (citing Targum Onkelos) and Targum Yonasan: It means 'If she (the mother) gives birth to a male'.
Seforno: It means that it is via the part of the firstborn calf and lamb that go on the Mizbe'ach - which are called 'Zikaron' that the owner will be remembered.
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
Having written "ve'Chol Mikn'cha Tizachar", why does the Torah need to add Petter Shor va'Seh"?
Bechoros, 6a: To teach us that all animals apart from those listed are not subject to the Bechorah - because "Kol Mikn'cha Tizachar" is a K'lal, and "Shor Seh va'Chamor", a P'rat, and 'K'lal u'Perat, Ein bi'Chelal Ela Mah she'bi'Perat' - (When a K'lal and P'rat are not followed by a K'lal, the P'rat is exclusive).
