Evaluate the following: ` |[1,x,y],[1, x+y, y],[1, x, x+y]| `

Explanation

To evaluate the determinant \( D = \begin{vmatrix} 1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y \end{vmatrix} \), we can use elementary row operations to simplify the determinant. Here is a step-by-step solution:

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

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