Answer
$x^5(x-1)(x^2+x+1)$
Work Step by Step
Factor out $x^5$.
$x^8-x^5\\
=x^5(x^3-1)$
$=x^5(x^3-1^3)$
Use special formula $a^3-b^3=(a-b)(a^2+ab+b^2)$ with $a=x$ and $b=1$ to obtain:
$=x^5(x-1)(x^2+(x)(1)+1^2)$
$=x^5(x-1)(x^2+x+1)$
Hence, the completelly factored form of the given expression is $x^5(x-1)(x^2+x+1)$.
