Well, i'm not english but i think the first sentece would be better using "with" and when the verb is in passive then you put "by" because.. YOU cut it using a knife, so, WITH a knife but it has been cut BY a knife, and i don't know if you could say "it has been cut with a knife" in spanish it doesnt matter whether by or with, but usually when the passive, you use "by" in english
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