Is there something that studies equivalent forms of writing and expression?

Question

Supose we have: $x^2+x$, one could write it as $x(x+1)$ which would be equivalent to the first expression. I guess there might be a finite number of ways of writing expressions such that they are equivalent.

Is there a field of study that studies arbitrary ways to express the same formula?

Answer 1

Surely a part of CA - computer algebra.