In short, 备课 is the preparation done by the teacher for the class, while 预习 is the preparation done by the students for the class.
More specifically, 备课 (bèi kè) generally refers to the process of preparing the actual content of the lesson, such as selecting and organizing materials, creating handouts or visual aids, and planning the structure of the class. Whereas 预习 (yù xí) refers to the process of previewing or reviewing the content that will be covered in the upcoming class - (students) reading assigned materials, reviewing lecture notes, and familiarizing (themselves) with the concepts that will be discussed.
Hope this helps.
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