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

Explanation

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

### Step 1: Base Case
We start with the base case where \( n = 1 \).

\[ x^{2 \cdot 1} - y^{2 \cdot 1} = x^2 - y^2 \]
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