8 Kai is proving that \(n ^ { 3 } - n\) is a multiple of 3 for all positive integer values of \(n\). Kai begins a proof by exhaustion.
Step 1 $$n ^ { 3 } - n = n \left( n ^ { 2 } - 1 \right)$$ Step 2 When \(n = 3 m\), where \(m\) is a \(n ^ { 3 } - n = 3 m \left( 9 m ^ { 2 } - 1 \right)\) non-negative integer which is a multiple of 3 Step 3 When \(n = 3 m + 1\), $$\begin{aligned} & n ^ { 3 } - n = ( 3 m + 1 ) \left( ( 3 m + 1 ) ^ { 2 } - 1 \right)
& = ( 3 m + 1 ) \left( 9 m ^ { 2 } \right)
& = 3 ( 3 m + 1 ) \left( 3 m ^ { 2 } \right) \end{aligned}$$ Step 5 Therefore \(n ^ { 3 } - n\) is a multiple of 3 for all positive integer values of \(n\) 8

1. Explain the two mistakes that Kai has made after Step 3. Step 4 \section*{which is a multiple of 3
   which is a multiple of 3}
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   别
   all positive integer values of \(n\) \section*{a} \includegraphics[max width=\textwidth, alt={}]{b7df05bf-f3fc-4705-a13c-6b562896fa9f-10_58_49_1037_370} 墐 pount \(\_\_\_\_\)
   \(\_\_\_\_\) " \(\_\_\_\_\)
   8
2. Correct Kai's argument from Step 4 onwards.