Why isn’t factoring x^4 - 81 as (x^2 + 9)(x^2 - 9) a complete factorization?

Step 1
Given statement is
${\displaystyle x^4-81as(x^2+9)(x^2-9)}$ is complete factorization.
Step 2
${\displaystyle \because (x^2-9)}$ factors are also possible.
${\displaystyle \therefore (x^2+9)(x^2-9)}$ is not complete factorization of ${\displaystyle x^4-81}$.
Step 3
${\displaystyle \because Factorsof(x^2-9)}$ are
${\displaystyle (x^2-9)=(x+3)(x-3)}$
${\displaystyle \therefore Completefactorizationof{x}^4-81is(x^2+9)(x+3)(x-3)}$.