Answer
$x^3-y^3=(x-1)(x^2+x+1)$
Work Step by Step
The given expression can be written as:
$=x^3-1^3$
RECALL:
A sum or difference of two cubes can be factored using the following:
(i) $a^3-b^3=(a-b)(a^2+ab+b^2)$
(ii) $a^3+b^3 = (a+b)(a^2-ab+b^2)$
Use formula (1) above with $a=x$ and $b=1$ to have:
$=(x-1)(x^2+x(1)+1^2)
\\=(x-1)(x^2+x+1)$