The massacre of the entire family of a vanquished and slain king is more common in those days. Such a total execution prevents revenge from the family of the murdered monarch. But of course, this act causes a lot of suffering and gives the new king a negative reputation as a cruel, ruthless ruler from the beginning. Such an act also lays in the heart of the new leader a seed of doubt, suspicion: if you yourself have killed your predecessor and his family, what will happen to you and your family in due course? Always watchful, never at peace.
The sin of Jeroboam was the worship of the calf in Bethel and Dan, intended to be a copy of the priest and temple worship in Jerusalem. For the origin of this see 1 Kings 12:26–32. The sin of idol worship is contagious: the spark of Jeroboam is spreading over the people.
On the prophet Ahijah and his ominous prophecy, see 1 Kings 14:1–16. Strictly speaking, 1 Kings 15:29–30 does not state that Baasha was commanded by God to kill the entire family of Jeroboam.
The word here translated provoke
can also be rendered defy,
incentivize,
challenge,
and is often used with the sin of worshipping images. We also encounter this word in 1 Kings 16:2, 1 Kings 16:7.
29 And as soon as he was king, he killed all the house of Jeroboam. He left to the house of Jeroboam not one that breathed, until he had destroyed it, according to the word of the LORD that he spoke by his servant Ahijah the Shilonite.