Answer
$(x^2+1)(x+1)(x-1)$
Work Step by Step
Write $x^4$ as $(x^2)^2$ and $1$ as $1^2$ to obtain:
$=(x^2)^2-1^2$
Use special formula $a^3-b^2=(a+b)(a-b)$ with $a=x^2$ and $b=1$ to obtain:
$=(x^2+1)(x^2-1)$
$=(x^2+1)(x^2-1^2)$
Use special formula $a^3-b^2=(a+b)(a-b)$ with $a=x$ and $b=1$.
$=(x^2+1)(x+1)(x-1)$
Hence, the completely factored form of the given expression is $(x^2+1)(x+1)(x-1)$.
