1. Simplify: $\frac{a^{3}-a^{2} b-a b^{2}+b^{3}}{a^{2}-2|a b|+b^{2}}=$
$\begin{array}{l}\text {1. }\left\{\begin{array}{ll}b, & a=0, b \neq 0 ; \\ \frac{(a-b, b)^{2}}{a+b}, & a b \neq 0, b=0 .\end{array}\right. \\ \text { Original expression }=\frac{a^{2}(a-b)-b^{2}(a-b)}{|a|^{2}-2|a||b|+|b|^{2}} \\ =\frac{(a-b)^{2}(a+b)}{(|a|-|b|)^{2}} \\ =\left\{\begin{array}{ll}b, & a=0, b \neq 0 ; \\ a+b, & a b>0 ; \\ \frac{(a-b)^{2}}{a+b}, & a b<0 ; \\ a, & a \neq 0, b=0 .\end{array}\right.\end{array}$