What is the meaning of "Chamasah"?
'Rashi': The war was in Chamas, and David struck him in Chamas. Radak - Hadad'ezer was there, for he had fought To'u, Melech Chamas (verses 9-10).
Who was going?
Radak, Malbim: Hadad'ezer.
Vilna Gaon: David.
What is the meaning of "b'Lechto Lehatziv Yado"?
'Rashi': He wanted to show his strength, to return his border [to the Peras river]. It says that Avshalom 'va'Yatzev Lo v'Chayav... va'Yikra Lo Yad Avshalom" (Shmuel II, 18:18), i.e. the strength of the border of Avshalom. Alternatively, he drew the form of his hand on the Matzevah. I heard so from R. Yitzchak bar Shmuel.
Radak: Hadad'ezer went to conquer and establish his border [on the Peras river].
Vilna Gaon: David went to erect a sign of his border.
Refer to 8:3:4:1-3.
Why does it say here "Lehatziv Yado", and in Shmuel II, 8:3 it says "Lehashiv Yado"?
Radak (here and Shmuel II, 8:3): Both of these mean the same. Initially Hadad'ezer helped Yisrael, and now he took from their land. This is why David said (Tehilim 60:3-4) "Elokim Zenachtanu Peratztanu...; Hir'ashtanu Eretz Petzamtah..." Now he wanted to establish his border until the place he conquered from Eretz Yisrael near the Peras river. David overpowered him with Hashem's help, and struck him.
Malbim: Hadad'ezer had gone to capture Chamas, Lehashiv (from there he would turn) to the Peras river to approach Eretz Yisrael. Ezra explained here that his intent was to establish his hand (authority, there).
Malbim (Shmuel II, 8:3): Hadad'ezer ruled over the [land near] the Peras river, close to the border of Yisrael. He had a Yad, i.e. a building with the form of a hand on it, to show that he conquered it with his hand, like it says [about Sha'ul] "v'Hinei Metziv Lo Yad" (Shmuel I, 15:12). David removed this building, and Hadad'ezer went to return Lehatzivo, i.e. to conquer the area.
