Prove, using properties of determinants: `|[y+k, y, y],[ y, y+k, y],[ y, y, y+k]|=k^2(3y+k)`

Explanation

To prove the determinant \( |[y+k, y, y],[y, y+k, y],[y, y, y+k]| = k^2(3y+k) \), we will use properties of determinants step by step.

### Step 1: Write the Determinant
We start with the determinant:
\[
D = \begin{vmatrix}
y+k & y & y \\
y & y+k & y \\
...