## Intermediate Algebra (6th Edition)

$\dfrac{m^{3}-n^{3}}{m-n}=m^{2}+mn+n^{2}$
$\dfrac{m^{3}-n^{3}}{m-n}$ The numerator is a difference of cubes. Factor it: $\dfrac{m^{3}-n^{3}}{m-n}=\dfrac{(m-n)(m^{2}+mn+n^{2})}{m-n}=...$ Simplify by removing the factors that appear both in the numerator and in the denominator of the resulting expression: $...=m^{2}+mn+n^{2}$