Without expanding evaluate the determinant `=|265 240 219 240 225 198 219 198 181|` .

Explanation

To evaluate the determinant

\[ D = \begin{vmatrix} 265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181 \end{vmatrix} \]

without expanding, we will perform a series of transformations on the columns and rows.

### Step 1: Transform the columns
We will first perform the following transformations:
- \( C_1 \leftarrow C_1 - C_3 \)
- \( C_2 \leftarrow C_2 - C_3 \)

This does not change the value of the determinant.

Calculating the new columns:
- For \( C_1 \):
\[ 265 - 219 = 46, \quad 240 - 198 = 42, \quad 219 - 181 = 38 \]
- For \( C_2 \):
\[ 240 - 219 = 21, \quad 225 - 198 = 27, \quad 198 - 181 = 17 \]

So, the determinant now looks like:
\[ D = \begin{vmatrix} 46 & 21 & 219 \\ 42 & 27 & 198 \\ 38 & 17 & 181 \end{vmatrix} \]

### Step 2: Further transformations
Next, we will perform the following transformations:
- \( C_1 \leftarrow C_1 - 2C_2 \)
- \( C_3 \leftarrow C_3 - 10C_2 \)

Calculating the new columns:
- For \( C_1 \):
\[ 46 - 2 \cdot 21 = 46 - 42 = 4, \quad 42 - 2 \cdot 27 = 42 - 54 = -12, \quad 38 - 2 \cdot 17 = 38 - 34 = 4 \]
- For \( C_3 \):
\[ 219 - 10 \cdot 21 = 219 - 210 = 9, \quad 198 - 10 \cdot 27 = 198 - 270 = -72, \quad 181 - 10 \cdot 17 = 181 - 170 = 11 \]

So, the determinant now looks like:
\[ D = \begin{vmatrix} 4 & 21 & 9 \\ -12 & 27 & -72 \\ 4 & 17 & 11 \end{vmatrix} \]

### Step 3: Row transformations
Now, we will perform the following row transformations:
- \( R_1 \leftarrow R_1 - R_2 \)
- \( R_3 \leftarrow R_3 - R_2 \)

Calculating the new rows:
- For \( R_1 \):
\[ 4 - (-12) = 16, \quad 21 - 27 = -6, \quad 9 - (-72) = 81 \]
- For \( R_3 \):
\[ 4 - (-12) = 16, \quad 17 - 27 = -10, \quad 11 - (-72) = 83 \]

So, the determinant now looks like:
\[ D = \begin{vmatrix} 16 & -6 & 81 \\ -12 & 27 & -72 \\ 16 & -10 & 83 \end{vmatrix} \]

### Step 4: Factor out common elements
From the first row, we can factor out 2:
\[ D = 2 \cdot \begin{vmatrix} 8 & -3 & 40.5 \\ -12 & 27 & -72 \\ 16 & -10 & 83 \end{vmatrix} \]

From the second row, we can factor out 3:
\[ D = 2 \cdot 3 \cdot \begin{vmatrix} 8 & -3 & 40.5 \\ -4 & 9 & -24 \\ 16 & -10 & 83 \end{vmatrix} \]

### Step 5: Identify equal rows
Notice that after the transformations, rows \( R_1 \) and \( R_3 \) have become equal. Thus, the determinant evaluates to 0.

### Final Result
Therefore, the value of the determinant \( D \) is:
\[ D = 0 \]