Learn Russian: Выполняя эту задачу, мы слушали фоновую музыку. - Performing this task, we listened to background music.

No, that would be grammatically incorrect in Russian. The core rule for verbal adverbs (like выполняя) is that they must share the exact same subject as the main verb. In the original sentence, мы (we) is the subject of both "listened" and "performing". If you made "music" the subject of the main clause, the sentence would imply the music itself was performing the task!

Why use the specific form выполняя here instead of выполнив?

Выполняя is an imperfective verbal adverb. It is used here because the action of "performing" happens simultaneously with the main action of "listening" (слушали). If you used the perfective form выполнив, it would mean "having performed"—implying you finished the task completely before you started listening to the music.

Is the comma after задачу optional?

No, it is mandatory. In Russian, a verbal adverb and its dependent words (like эту задачу) form a phrase called a деепричастный оборот. These phrases must always be set off by commas, no matter where they appear in the sentence.

Why do both задачу and музыку take the accusative case here?