Factor u^3-u^2v+uv^2-v^3

$u^{3} - u^{2} v + u v^{2} - v^{3}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(u^{3} - u^{2} v) + u v^{2} - v^{3}$

Factor out the greatest common factor (GCF) from each group.

$u^{2} (u - 1 v) + v^{2} (u - v)$

Factor the polynomial by factoring out the greatest common factor, $u - 1 v$ .

$(u - 1 v) (u^{2} + v^{2})$

Rewrite $- 1 v$ as $- v$ .

$(u - v) (u^{2} + v^{2})$