Does anybody knows the difference between じゃありませんでした and ありませんでした? im quizzing some grammar on the site and the task is to give the polite past negative.From any other source i looked up so far they say that the first is less polite than the second but i think that its not the case here..
Ok, I may be wrong as I'm kind of early in this japanese journey, but as far as I know, ありませんでした is the negative past of ある in a polite way, whereas じゃありませんでした is the negative past of である, which would have the same meaning as じゃなかった. What might be troubling you is that じゃ at the start, which is no more than ではin a less polite fashion.
So, to sum up:
ある - ありません - ありませんでした
である (same meaning as だ, but kind of formal) ー ではありません - ではありませんでした (じゃありませんでした)
Given that I may be completely wrong, someone please correct me if that's the case :-[
ありません means "is not": I'm not cold, it's not difficult, etc. But it's not specifically identifying anything, only giving a state or a quality. では connotes something settled, something certain. である means you're identifying some thing as a particular thing. 吾輩は猫である "I am a cat" (Title of Souseki's novel). ではありません means what you're talking about isn't a certain thing: その動物は猫ではありません。That animal is not [b]a[/b] cat. Casually, 猫じゃありません。(The animal) It's not a cat. でした is just the past tense of です, which has to go on the back of ありません to form the past. 猫じゃありませんでした。"It wasn't a cat."