Jamieson, Fausset and Brown on Jeremiah 3:8

8. I saw that, though (whereas) it was for this very reason (namely), because backsliding (apostate) Israel had committed adultery I had put her away (2Ki 17:6, 18), and given her a bill of divorce, yet Judah, &c. (Eze 23:11, &c.).

bill of divorce--literally, "a writing of cuttings off." The plural implies the completeness of the severance. The use of this metaphor here, as in the former discourse (Jr 3:1), implies a close connection between the discourses. The epithets are characteristic; Israel "apostate" (as the Hebrew for "backsliding" is better rendered); Judah, not as yet utterly apostate, but treacherous or faithless.

also--herself also, like Israel.