"For you shall utterly destroy them"—Deuteronomy 20:17.
We are commanded to kill the members of the Seven Canaanite Nations—to utterly eradicate them. This because they were the original source of idolatry and its prime practitioners. In many places the Torah encourages and urges us to observe this mitzvah, and explains the reason for this mitzvah: so that we should not learn from these nations' heretical ways. The battle against the Canaanite nations is considered a "mitzvah battle."
This mitzvah was fully completed by King David, who killed the remaining members of these nations that had survived till his day, besides for a few who scattered and were absorbed into other nations.
[Translator's Note: In the Laws of Kings, Maimonides explains that the killing of the Seven Nations was a last resort, only done if the nations refused to evacuate the Holy Land, or to remain, but reject idolatry and accept upon themselves Jewish sovereignty.]
"You shall not leave a soul alive"—Deuteronomy 20:16.
We may not allow even one individual from the Seven Canaanite Nations to live, for they would have a negative effect on the Jewish inhabitants of the land and influence them to worship idols.
[For more on this mitzvah, see Positive Commandment 187.]
"You shall erase the memory of Amalek"—Deuteronomy 25:19.
We are commanded to wipe out the descendants of Amalek, men and women, old and young.
This is one of the three mitzvot the Jews were commanded upon entering the land—the other two were appointing a king and building the Holy Temple.
"Remember what Amalek did to you"—Deuteronomy 25:17.
We are enjoined to remember that which Amalek did to us, that they were the first to "greet" us [after we left Egypt] with evil [i.e., battle]. We must verbally recall this at all times, and awaken our souls to battle them. We must call upon people to hate them, so that the matter not be forgotten, and the hate should not abate with the passage of time.
"You must not forget"—Deuteronomy 25:19.
We are enjoined to never forget that which Amalek did to us, that they were the first to "greet" us [after we left Egypt] with evil [i.e., battle]. We must never allow the hate from Amalek to be forgotten from our hearts.
