Answer
$(9x^{2}+1)(9x^{2}-1)$
Work Step by Step
If $a$ and $b$ are real numbers, we know that $a^{2}-b^{2}=(a+b)(a-b)$. In words, the difference of the squares of two terms factors as a product of a sum and a difference of those terms.
Therefore, we know that $81x^{4}-1=(9x^{2}+1)(9x^{2}-1)$. In this case, $a=9x^{2}$ and $b=1$.
