Answer
$(x^2+9)(x+3)(x-3)$
Work Step by Step
Write $x^4$ as $(x^2)^2$ and $81$ as $9^2$ to obtain:
$x^4-81=(x^2)^2-9^2$
Use special formula $a^3-b^2=(a+b)(a-b)$ with $a=x^2$ and $b=9$ to obtain:
$=(x^2+9)(x^2-9)$
$=(x^2+9)(x^2-3^2)$
Use special formula $a^2-b^2=(a+b)(a-b)$ with $a=x$ and $b=3$ to obtain:
$=(x^2+9)(x+3)(x-3)$
Hence, the completely factored form of the given expression is $(x^2+9)(x+3)(x-3)$.
