Thou answeredst them, O Lord our God - The reference here is to God as “our” God; that is, the language used by those who now worship him is designed to give encouragement in approaching his throne. The God that “we” worship is the same that “they” worshipped; and as he answered them, we may feel assured that he will answer us.
Thou wast a God that forgavest them - They were not perfect; they were sinners; they often offended thee, and yet thou didst answer them, and show them mercy.
Though thou tookest vengeance - Though thou didst manifest thy displeasure at their misconduct; though thou in thy judgments didst show that thou wast displeased with them; nevertheless thou didst answer them. Sinners as they were, and often as thou didst show thy displeasure at their conduct, yet thou didst hear their prayers and bless them.
Of their inventions - The Hebrew word denotes work, deed, doing, conduct. It means here what they did - their sins. There is no allusion to any special art or “cunning” in what they did - as if they had “invented” or found out some new form of sin.