Should I include obvious steps in mathematical paper?

Always best to error on the side of providing "too much" information, than not enough. If the examiner is trained in mathematics, then you could probably get by without providing excessive detail.

But take care not to assume "too much" in the way of what you think others will know. What is "obvious" is in "the eye of the beholder." In the example you provide, I'd suggest including at least an intermediate step or explanation as to why the left-hand side follows from right hand side of your equation.

The important thing, of course, is that you understand what you are doing.
But you also want to take care to ensure others understand what you are saying.
And certainly not least, you want to be sure that others (as in examiners) understand that you understand what you are saying!

First, if this is an examination in which you will be awarded marks, you need to find out from the examiner what can be omitted.

Second, what is obvious to one may not be to another, so you need to write in such a way that it caters to your intended audience.

In your example, assuming it is the IB, it would be good to fill in the missing steps as it is not immediately obvious why equality holds.

I am not a mathematician, but I teach engineering and computer science, and I've read quite a number of papers and reports from students. I don't know if this is just me being particularly lazy, but I'd rather avoid having to decode things that are only "sort of" obvious, or that I need pen and paper to get through.

When a student has worked with a project, maybe for months, many things seem obvious to that student, so they omit them from the report or paper. Perhaps they even feel ashamed to put such very simple things in their text. But the things that are obvious to someone who has just spent weeks or months on them, sometimes are much less obvious to another reader.