Since Jews have been reciting this berakha for generations, Rav Yehuda’s ruling hardly comes as a surprise. Nevertheless it is an important statement, as one could argue that the search is merely preparation for destroying the hametz, or even that the actual mitzva is that no hametz should be found in one’s house, so even destroying the hametz is simply preparation for that. The Rosh says that Rav Yehuda is teaching a valuable lesson – that the bedika (search) is an essential part of the mitzva of bi’ur (burning), so the berakha should be recited on it. According to the Maharam Halava, the Biblical obligation is the search for hametz; destroying the hametz is only a Rabbinic decree.
There are two different opinions about the version of the blessing that is said. The blessing begins with the traditional introductory words “Blessed are you, Hashem, our God, King of the world, who has commanded us…”
Rav Pappi quotes Rava as requiring one to conclude with the words leva’er hametz – to remove leavened bread.
Rav Pappa quotes Rava as requiring that one say at the end al bi’ur hametz – concerning the removal of leavened bread.
The Gemara concludes that the berakha that should be made is al bi’ur hametz. Based on the discussion in our Gemara, the rishonim attempt to find general rules that would reliably indicate when the berakha that precedes the act of performing a mitzva should be said as la’asot – an expression that we are commanded “to do” the mitzva and when we should say al mitzvat that we are commanded “on the mitzva of…”
According to Rabbenu Tam, it depends how quickly the mitzva will be performed. When the mitzva is done immediately after the berakha we say al mitzvat; if there will be a gap between the berakha and the mitzva we say la’asot.
According to the Ramban, a mitzva that can be done via a messenger gets the al mitzvat blessing; when a mitzva must be done by the individual, he says la’asot.
Rabbenu Yehonatan argues that a mitzva that is done once is blessed as la’asot, while a mitzva that will be done many times receives the al mitzvat blessing.