What is the meaning of "va'Yhi ba'Davar ha'Zeh l'Chatas Beis Yaravam"?
Radak #1: This caused the punishment of Beis Yaravam, to be destroyed. This is like "Zos Tihyeh Chatas Mitzrayim" (Zecharyah 14:19). Ba'Davar is like ha'Davar.
Radak #2: In this matter there was Hashem's anger against Beis Yaravam. He did not repent in spite of everything he saw!
Why will all of Beis Yaravam be destroyed?
Malbim: This is like it says, "v'Samti 1 Es Panai ba'Ish ha'Hu uv'Mishpachto" (Vayikra 20:5).
Editions in which it says "v'Eten" are mistaken. That is Vayikra 20:3, which does not mention uv'Mishpachto! (PF) Even though the verse discusses Molech, some say that 'Molech' encompasses all idolatries (in Ramban there).