At PrepScholar, we call our answers / solution manuals “Teaching Explanations”, because we believe answers should be geared to teaching you how to tackle the question. This is why we answer your questions in up to four different ways. Let’s go over the different types and what they mean.
This is the short and technically correct answer you’ll sometimes see in official solution manuals. It’s correct, but often can leave you without knowing where to start. Also, it makes for a poor problem set / homework answer. If I were a math professor, this is what I would put to show another math professor I know my materials.
As a professor, this is the answer that I’d expect on my students’ problem sets and homework in order to get an A. You not only have to get the answer, but also “show your work”. What I’m looking for is that you know the right way to get the answer.
While homework answers will get you an A, it might not be the best for actually understanding the question, and to make sure you get an A on the final exam. The problem with homework-quality answers is that it proves to someone who is more knowledgable that you that you know your materials. It doesn’t provide the motivation for how to get to the answer!
This is the best place to start to truly understand the solution. It’s a “authentic mental walkthrough” of all the steps that a new student learning the material for the first time should be sequentially thinking about. It teaches you how to think so that not only do you solve this problem, but you also learn to solve other similar questions.
This is a video of an impromptu explanation. It’s meant to mimic the motivated answer, and sometimes can fit into homework answer category. Videos will often contain extra details that can help you, so if the motivated answer doesn’t do it for you, watch the video too!