We are to find the quotient of the expression;
[tex]\frac{m^8-1}{m-1}[/tex][tex]\begin{gathered} m^8-1=(m^4)^2-(1^4)^2=(m^4-1)(m^4+1) \\ m^4-1=(m^2)^2-(1^2)^2=(m^2-1)(m^2+1) \\ m^2-1=(m+1)(m-1) \end{gathered}[/tex]
Therefore;
[tex]\begin{gathered} \frac{m^8-1}{m-1}=\frac{(m+1)(m-1)(m^2+1)(m^4+1)}{m-1} \\ =(m+1)(m^2+1)(m^4+1) \end{gathered}[/tex]
Thus the quotient is;
[tex](m+1)(m^2+1)(m^4+1)[/tex]
