What do we learn from "Bechah"?
Radak: It means 'with Your help.' 1
Malbim (Tehilim 18:30): Hashem Himself protects from mishaps and gives victory to those who fear Him. His salvation does not depend on great or small (armies) - "Lo bi'Gevuras ha'Sus Yechpatz
Radak: "Bechah" is written with Chaf Hei at the end, in place of final Chaf. We find like this, e.g. "u'Vechah uv'Amecha" (Shemos 7:29), "ha'Nitzeves Imechah" (Shmuel I, 1:26). Usually, it is written without a Hei.
What is the meaning of "Arutz"?
Radak #1: The root is Ratzatz (I will crush the troop). It has a Shuruk, like "Yarun v'Some'ach" (Mishlei 29:6), "Yashud Tzaharayim" (Tehilim 91:6).
Radak #2: I will run [to the troop of my enemies, without fear].
Radak citing Targum Yonasan: [With Your word] I will amass [many troops].
Why does it say "Adaleg Shur"?
Rashi (Tehilim 18:30, from Shochar Tov 18): When David came to fight against Yevusi, he said "whoever strikes Yevusi will be a head and officer" (Divrei ha'Yamim I, 11:6). Yo'av brought a Berush (pine) tree and bent it. Yo'av hung on it, and [when they let it spring back] jumped onto the top of the wall. David said "Yehelmeni Tzadik Chesed" (Tehilim 141:5); Hashem lowered the wall, and David jumped [over it].
Radak, Malbim (Tehilim 18:30): I will jump over the wall of the city of my enemies to conquer them. Radak - Adaleg shows how quickly he will conquer them, as if he enters them amidst jumping.
Why did David have such confidence of victory?
Mesilas Yesharim (Perek 10): It is because he was careful and cleansed himself totally. Yehoshafat, Asa and Chizkiyah were not so confident, because they were not as clean as David. For this reason, David asked to totally eradicate his enemies (verse 38), and they did not.
