Factor the expression \(x^{6}-81 x^{2}\)completely.
Explanation
In factoring \(x^{6}-81 x^{2}\), we initially get
\(x^{2}\left(x^{4}-81\right)\)which can be factored further to
\(x^{2}\left(x^{2}+9\right)\left(x^{2}-9\right)\)
The question requires complete factoring and we see that
\(\left(x^{2}-9\right)\) can still be factored to \((x-3)(x+3)\).
Therefore, the correct answer is \(x^{2}\left(x^{2}+9\right)(x-3)(x+3)\).
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