Indeed, we have already brought the words of the Rabbi Nissim (RaN) who explains this, and it is because individually it is not sufficient, for if one nullifies it alone, perhaps he will not nullify it with a complete heart, and if he burns it alone, perhaps he will find a beautiful piece of leaven after the time of prohibition and change his mind about it. And so the Mishnah Berurah explains clearly (Siman Tav Tet, seif 6): "Immediately at nightfall one should nullify it. The reason is that even though according to Torah law, checking alone is sufficient, for from the Torah, it suffices with one of them, either by burning or by nullifying, for even if some leaven remains in the house, he does not transgress as long as he did not know, since he checked thoroughly and did everything that was required of him. Nevertheless, the sages were concerned that he might find a beautiful piece of leaven that does not nullify itself like crumbs, and he would delay a little before burning it and transgress without realizing it. But if he nullifies it, he does not transgress in any way without realizing it, for it becomes ownerless and is not his responsibility."