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What is the difference between
Die Rechnung ist noch nicht geschrieben worden.
and
Die Rechnung konnte noch nicht geschrieben werden.
Why is it worden in the first case and werden in the second case? Naively, I woul also use worden in the second case.
In the first sentence the passive voice was used - in the Perfekt tense. The basic form of werden in Perfekt is:
ist geworden
The "ge-" is dropped in the passive voice, because we would normally have two words with "ge-" in a row.
ist gemacht
geworden
This rule applies even if there is no "ge-" in the first word.
ist beschrieben
geworden
The second sentence uses the modal verb "können" (can) in past tense, after which we have to use the infinitive form (exactly like in English: could not be written yet) - and this "be written" is translated as "geschrieben werden".
I hope it was understandable.
In addition to the grammatical reasons outlined by Barth, I'd like to point out a difference in meaning:
"Die Rechnung ist noch nicht geschrieben worden." would be used to indicate that the invoice has not, yet, been written. Just stating that it was not written, period.
"Die Rechnung konnte noch nicht geschrieben werden." would be used to indicate that one would have wanted to write the invoice, but that for some reason it has not, yet, been possible. The sentence would include a hint of an excuse, indicating that one is somewhat sorry for the fact, that it hasn't been written, yet.
