In my native language, we often talk about (what could be literally translated as) “modifying” or “refining” mathematical equations and expressions into a different form. Example sentences could be something like:
(All these “refinements” are implied to result in expressions which are equivalent to the original, yet simpler or having different qualities.)
I don't think I ever hear something like this in English, usually people use less direct expressions (“find the factored form“, without emphasis on the original expression) or more specific expressions (“factor the polynomial”, “substitute into the equation”). I often struggle to translate such sentences, because I often need to put emphasis on both the original expression being refined and the requested final form, but without being specific about the method.
Is any of the given sentences valid in English? Is there a natural way to say something like this?