What is the meaning of "va'Yarev ba'Nachal"?
Rashi: He fought in the valley. Radak - this is from the root Riv (quarrel).
Rashi citing Yuma 22b: He judged about matters of [Eglah Arufah, which is beheaded in] a valley. If for one murdered soul, the Torah says to behead a calf [to atone], all the more so for all these! If a person sinned [and must be killed], did the animals sin?! 1
Radak: This is from the root Arav (ambush). This is Hifil, just the Aleph is omitted. Alternatively, it is Dagush (Pi'el), like va'Ye'erav; the Kamatz under the Yud supports this. The Aleph is omitted due to the Kamatz under the Yud.
Targum Yonasan: He arranged his camp in the valley.
Malbim: Kings do not normally make war without a pretext - "Mah Li va'Lach Ki Vasa Elai Lehilachem" (Shoftim 11:12). Sha'ul made a quarrel 2 , and said that the valley in front of Amalek's cities belongs to Yisrael. Amalek contested this, and this was the reason for the war. He erred. He did not need a reason other than Hashem's command - "Mesan'echa Hashem Esna" (Tehilim 139:21)!
Yuma 22b: A Bas Kol (voice from Heaven) said "Al Tehi Tzadik Harbeh" (Koheles 7:16)! Radak - i.e. do not try to be more righteous than your Creator!
Why was it not enough that Amalek attacked Yisrael twice in the Midbar? Perhaps it is because we already fought them and 'finished' those matters. (PF)