Positive Mitzvah 187
Destroying the Seven Idol-Worshiping Nations
Deuteronomy 20:17 "But you shall utterly destroy them"
Every person is influenced by his neighbors.
The seven nations that occupied Eretz Yisrael before the nation of Israel conquered it, were corrupt idol-worshipers.
HaShem did not want them to live among the Jewish people and lead them astray. Therefore, He commanded us to wipe out these nations entirely.
Negative Mitzvah 49
You shall not allow any inhabitants of the Seven Nations of Canaan to live
Deuteronomy 20:16 "You shall not leave a soul alive"
The Torah instructs us to totally destroy the Seven Canaanite nations.
We must not be tempted to express greater compassion than HaShem, and out of sympathy, allow any members of these Seven Nations to live.
Positive Mitzvah 188
Total Destruction of Amalek
Deuteronomy 25:19 "You shall erase the memory of Amalek"
When the Jewish people came out of Egypt, all the nations of the world stood in awe of this great miracle.
They all heard of the greatness of HaShem and the many wonders He performed for His chosen people.
They were convinced that they would be powerless against the Jewish nation.
Only Amalek dared to challenge HaShem.
Foolishly, the Amalekites declared war and attacked the Jewish people. Needless to say, they were defeated, for HaShem Himself fought for the nation of Israel.
Nevertheless, their battle had a very negative effect on the future of the Jewish nation. Afterwards, other nations also dared to question the strength of this new people. Thus, despite their fall, the Amalekites did much damage.
The Rabbis compared this to a steaming bathtub, too hot for anyone to climb into. Then, someone came along and plunged into the boiling water. He got scorched, but in the process of doing so, he cooled the water a bit, enabling others to enter.
Because Amalek was the first nation to doubt HaShem's power, we are commanded to destroy it entirely.
Positive Mitzvah 189
Remembering What Amalek Did
Deuteronomy 25:17 "Remember what Amalek did to you"
HaShem does not want us to forget our hatred for Amalek.
He commands us to constantly remember their attack on our people and to tell others about it (see Negative Mitzvah 59).
Negative Mitzvah 59
You shall not forget what Amalek did
Deuteronomy 25:19 "You must not forget"
The nation of Amalek is condemned forever (see Positive Mitzvah 189).
They showed their hatred towards HaShem and the Jewish people when they declared war upon us as we left Egypt.
Throughout all the generations, their descendants have continued to maintain this hatred towards us.
We are commanded never to forget the evil they have done to us.