Question

find the binomial that completes the factorization.
$u^3 - v^3 = (\boxed{})(u^2 + uv + v^2)$

Explanation:

Step1: Recall difference of cubes formula

The difference of cubes identity is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

Step2: Match given expression to formula

Here, $a = u$ and $b = v$. Substitute into the identity:
$u^3 - v^3 = (u - v)(u^2 + uv + v^2)$

Answer:

$u - v$