Question

factor.
$u^3 - 1$

Explanation:

Step1: Identify difference of cubes

Recall formula: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$
Here, $a = u$, $b = 1$ since $1 = 1^3$.

Step2: Substitute into formula

Substitute $a=u$, $b=1$ into the difference of cubes formula:

$$\begin{aligned} u^3 - 1^3 &= (u - 1)(u^2 + (u)(1) + 1^2) \end{aligned}$$

Step3: Simplify the second factor

Calculate the terms in the quadratic factor:
$u^2 + u + 1$

Answer:

$(u - 1)(u^2 + u + 1)$