Prove that `sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)]` .

Explanation

To prove that \( \sqrt{10} \left( (\sqrt{10}+1)^{100} - (\sqrt{10}-1)^{100} \right) \) is an even number, we can use the Binomial Theorem.

### Step-by-step Solution:

1. **Understanding the Expression**:
We need to analyze the expression \( \sqrt{10} \left( (\sqrt{10}+1)^{100} - (\sqrt{10}-1)^{100} \right) \).

2. **Applying the Binomial Theorem**:
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