Answer
$(9x^2+1)(3x+1)(3x-1)$.
Work Step by Step
An expression is factored completely if it is written as a product of factors so that none of its factors can be further factored.
Rewrite the given expression using perfect squares.
$81x^4-1=(9x^2)^2-1^2$
Use the algebraic identity $a^2-b^2=(a+b)(a-b)$.
$=(9x^2+1)(9x^2-1)$
Rewrite the second factor using perfect squares:
$=(9x^2+1)[(3x)^2-1^2]$
Use the algebraic identity $a^2-b^2=(a+b)(a-b)$ again.
$=(9x^2+1)(3x+1)(3x-1)$.
