When we’re writing, we can use a thesaurus to find a different word with the same meaning to present an idea. How can we find different ways to present algebraic expressions without changing their meaning?

I can think of a couple of properties that can be used in order to present an expression without changing their meaning. The distributive, and the commutative property all change the expression in different ways, but maintain the same value.
For example, we have x^2+x=0. The commutative property allows us to flip the expression so that x+x^2=0.
As for the distributive property, we can change the expression so that x^2+x=0 would become x(x+1)=0.
All of these result are the same value but in a different presentation.