Prove the following by using the principle of mathematical induction for all `n in N`:`3^(2n+2)-8n-9`is divisible by 8.

Explanation

To prove that \(3^{2n+2} - 8n - 9\) is divisible by 8 for all \(n \in \mathbb{N}\) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We need to verify the base case, \(n = 1\).

\[ P(1) = 3^{2(1)+2} - 8(1) - 9 \]
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