The Gemara derives three prohibitions from 'lo techanem': (1) do not give them a settlement in the land, (2) do not show them favor (lo titen lahem chein), and (3) do not give them a free gift. This tripartite derivation is the foundational Talmudic source for all later halachic discussion of benefit to idolaters.
דְּאָמַר קְרָא: ״לֹא תְחׇנֵּם״, לֹא תִּתֵּן לָהֶם חֲנָיָיה בַּקַּרְקַע. הַאי ״לָא תְחׇנֵּם״ מִיבְּעֵי לֵיהּ, דְּהָכִי קָאָמַר רַחֲמָנָא: לֹא תִּתֵּן לָהֶם חֵן. אִם כֵּן, לֵימָא קְרָא ״לֹא תְחוּנֵּם״, מַאי ״לֹא תְחׇנֵּם״? שְׁמַע מִינַּהּ תַּרְתֵּי. וְאַכַּתִּי מִיבְּעֵי לֵיהּ, דְּהָכִי אָמַר רַחֲמָנָא: לֹא תִּתֵּן לָהֶם מַתְּנַת (שֶׁל) חִנָּם! אִם כֵּן, לֵימָא קְרָא ״לֹא תְחִינֵּם״, מַאי ״לֹא תְחׇנֵּם״? שְׁמַע מִינַּהּ כּוּלְּהוּ. תַּנְיָא נָמֵי הָכִי: ״לֹא תְחׇנֵּם״ — לֹא תִּתֵּן לָהֶם חֲנָיָיה בַּקַּרְקַע, דָּבָר אַחֵר: ״לֹא תְחׇנֵּם״ — לֹא תִּתֵּן לָהֶם חֵן, דָּבָר אַחֵר: ״לֹא תְחׇנֵּם״ — לֹא תִּתֵּן לָהֶם מַתְּנַת חִנָּם.
The source is that the verse states: “You should not show them mercy [lo teḥonnem]” (Deuteronomy 7:2), which is understood as meaning: You should not give them a chance to encamp [ḥanayah] in, i.e., to acquire land in, Eretz Yisrael. The Gemara asks: This phrase: “You should not show them mercy”; isn’t it necessary to teach that this is what the Merciful one is saying: You should not give them favor [ḥen] by praising them? The Gemara answers: If that were so, let the verse say: Lo teḥunnem, with the letter vav, as then it would be evident that this is a form of the root ḥet, vav, nun, which means favor. What is the reason that the verse instead states: Lo teḥonnem, without the letter vav? Conclude two conclusions from it, that one may not praise them and also that one may not allow them to acquire land. The Gemara asks: But still, isn’t the phrase “You should not show them mercy” necessary to teach the halakha that this is what the Merciful One states: You should not give them an undeserved [ḥinnam] gift? The Gemara answers: If that were so, let the verse say: Lo teḥinnem. What is the reason that it is spelled without the letter yud, as: Lo teḥonnem? Learn from it all of these three halakhot. This is also taught in a baraita: “You should not show them mercy”; this teaches that you should not give them a chance to encamp in the land of Eretz Yisrael. Another matter: “You should not show them mercy”; this indicates that you should not give them favor. Another matter: “You should not show them mercy”; this teaches that you should not give them an undeserved gift.