\begin{enumerate}
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\item (a) Expand \(( 1 + x ) ^ { 4 }\) in ascending powers of \(x\).
(b) Using your expansion, express each of the following in the form \(a + b \sqrt { 2 }\), where \(a\) and \(b\) are integers.
- \(( 1 + \sqrt { 2 } ) ^ { 4 }\)
- \(( 1 - \sqrt { 2 } ) ^ { 8 }\)
\item The second and fifth terms of an arithmetic sequence are 26 and 41 repectively.