Question

Not a graded or timed assessment. Need help, thank you. Please show work.

Answer 1

`(m^8-1)/(m-1)`

Apply exponent rules

`((m^4)^2-1)/(m-1)`

Apply difference of two square formula

`\begin{gathered} x^2-y^2=(x^{}-y)(x+y) \\ (m^4)^2-1^2=(m^4-1)(m^4+1) \end{gathered}`
`((m^4+1)(m^4-1))/(m-1)`

Apply exponent rule

`((m^4+1)(m^4-1))/(m-1)=((m^4+1)(m^2)^2-1^2))/(m-1)`

Apply difference of two square formula

`(m^2)^2-1^2=(m^2+1)(m^2-1)`
`((m^4+1)(m^2+1)(m^2-1))/(m-1)`

factor

`m^2-1=(m+1)(m-1)_{}`
`\frac{(m^4+1)(m^2+1)(m^{}+1)(m-1)}{m-1}`

Cancel the common factor (m-1)

The final answer

`(m^4+1)(m^2+1)(m^{}+1)`