GreylynV285787 GreylynV285787
  • 26-10-2022
  • Mathematics
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Please help. Not a timed or graded assignment. Quick response with work will get amazing review :))

Please help Not a timed or graded assignment Quick response with work will get amazing review class=

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AalayaE1356 AalayaE1356
  • 26-10-2022

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]

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