$\begin{array}{l}\phantom{\phantom{;}m\phantom{;}+1;}{-m^{7}+m^{6}-m^{5}+m^{4}-m^{3}+m^{2}-m\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}m\phantom{;}+1\overline{\smash{)}-m^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}m\phantom{;}+1;}\underline{\phantom{;}m^{8}+m^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}m^{8}+m^{7};}\phantom{;}m^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+1-;x^n;}\underline{-m^{7}-m^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-m^{7}-m^{6}-;x^n;}-m^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}m^{6}+m^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}m^{6}+m^{5}-;x^n-;x^n;}\phantom{;}m^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-m^{5}-m^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-m^{5}-m^{4}-;x^n-;x^n-;x^n;}-m^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}m^{4}+m^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;\phantom{;}m^{4}+m^{3}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}m^{3}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+1-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-m^{3}-m^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;-m^{3}-m^{2}-;x^n-;x^n-;x^n-;x^n-;x^n;}-m^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+1-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}m^{2}+m\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;;;\phantom{;}m^{2}+m\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}m\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+1-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-m\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;;;;;;;-m\phantom{;}-1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\\\end{array}$

$-m^{7}+m^{6}-m^{5}+m^{4}-m^{3}+m^{2}-m+1$