Evaluate the following: `\ {a^2+sqrt(a^2-1)}^4+{a^2-sqrt(a^2-1)}^4`

Explanation

To evaluate the expression \( {a^2 + \sqrt{a^2 - 1}}^4 + {a^2 - \sqrt{a^2 - 1}}^4 \), we can use the Binomial Theorem. Let's go through the solution step by step.

### Step 1: Recognize the Structure
The expression can be recognized as the sum of two binomial expansions:
\[ x = a^2, \quad a = \sqrt{a^2 - 1}, \quad n = 4 \]
Thus, we have:
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