The ḥametz that the Torah forbids is comprised of flour and water. If flour was kneaded with fruit juice – even if the dough sits a full day and rises – it is not considered ḥametz since rising of this kind is different from the type forbidden by the Torah. The category of “fruit juice” (“mei peirot”) includes wine, honey, milk, oil, and egg, in addition to all juices squeezed from a fruit, like apple or berry juice. Since fruit juice does not cause dough to become ḥametz, one may knead, bake, and eat such dough on Pesaḥ. Nevertheless, one would not fulfill the mitzva of matza on the first night of Pesaḥ with it, because the Torah calls matza “leḥem oni” (“poor man’s bread”), whereas matza made from fruit juice is “matza ashira” (“rich matza” – colloquially known in English as “egg matza”), since it possesses more than the taste of just flour and water.
If a drop of water gets mixed in with the fruit juice, the dough can become ḥametz. Moreover, according to many poskim, the combination of water and fruit juice actually expedites the leavening process. Thus, in order to avoid such doubts, the Sages prohibited kneading dough with a mixture of fruit juice and water during Pesaḥ (SA 462:1-3).
Ashkenazic custom is to prohibit eating anything made of dough kneaded with fruit juice out of concern that water mixed with the fruit juice, causing the dough to become ḥametz. Furthermore, it takes into account the opinion of Rashi, who disagrees with most Rishonim and maintains that fruit juice alone can cause something to become ḥametz on the rabbinic level. Although in principle it is possible to follow the lenient ruling of the vast majority of poskim, Ashkenazic custom, which should not be altered, is nevertheless strict, except in the case of the elderly and ill, where the custom is to be lenient (Rema 462:4). Nowadays, many Sephardic poskim also rule stringently, because it is known that water and other ingredients are generally added to fruit juice, increasing the likelihood that the egg matza became ḥametz (R. Mordechai Eliyahu).
The second sugya, on Pesaḥim 36a, concerns a tannaitic dispute about matza ashira on Pesaḥ. According to Rif and Rambam, the halakha follows R. Akiva that one is permitted to knead flour in a mix of fruit juice and water provided that one takes caution to prevent the mixture from becoming ḥametz, just as one would with a standard flour-water mixture. This is also the opinion of R. Natronai Gaon and Me’iri. Against them, many Rishonim maintain that one should not knead flour with fruit juice and water, since it turns into ḥametz faster than does flour and water, but they disagree about what to do be-di’avad. According to R. Hai Gaon and Behag, the halakha follows Rabban Gamliel that one is required to burn the kneaded dough. According to Rabbeinu Ḥananel, Ritz Gi’at, and Rosh, the halakha follows the Sages that if one bakes the dough very quickly, he is permitted to eat it. This is the ruling of SA 462:2.
Ashkenazic custom is to be strict out of concern for the view of Rashi and those who agree with him, who maintain that flour and fruit juice alone can become ḥametz, or out of concern that some water will mix with the fruit juice. The parameters of what is considered water and what is considered fruit juice are discussed in SA 462:3 and 7 and §466 (and see the Encyclopedia Talmudit entry “Ḥametz,” pp. 89-99). Regarding Sephardic custom, R. Mordechai Eliyahu had a long-standing opposition to certifying matza ashira as kosher for Pesaḥ out of concern that the fruit juice has been mixed with water or substances that have the status of water, like an agent that causes the dough to rise. (There are also grounds to forbid this because it catalyzes an action that resembles leavening, as explained in Pesaḥim 28a, in the commentary of Maharam Ḥalawa, and in Matza Ashira, p. 178.) Over time, it became apparent that his concern was justified, and water and occasionally even agents that cause the dough to rise are added to fruit juice. Nevertheless, some authorities rule leniently; according to them, these leavening agents do not cause the dough to become ḥametz. This ruling appears in Yabi’a Omer 9:42 and Shema Shlomo 4:13-17. However, according to many authorities these agents are forbidden by the Torah, or at least rabbinically, and therefore they prohibit Sephardim from eating factory-produced matza ashira on Pesaḥ.