An equivalent expression may look different but gives the same value for every permitted substitution. Algebraic manipulation is not arbitrary symbol movement: each step must preserve equivalence.
Distributivity connects factorised and expanded forms: a(b+c)=ab+ac. The same relationship works in reverse when factorising. Like terms combine only when their variable parts match exactly.
The AC9 elaborations use algebra tiles and area models to make these properties visible. Use the model to explain why a rewrite works, then compress the reasoning into symbolic steps.