`|(265,240,219),(240,225,198),(219,198,181)|=`

Options

A. 779
B. 679
C. 0
D. none

Answer

To find the value of the determinant

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

we can use the method of cofactor expansion along the first row.

### Step 1: Write the determinant

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

### Step 2: Calculate the 2x2 determinants

1. **First determinant**:

\[ \begin{vmatrix} 225 & 198 \\ 198 & 181 \end{vmatrix} = (225 \cdot 181) - (198 \cdot 198) \]

Calculating this:

\[ = 40725 - 39204 = 1521 \]

2. **Second determinant**:

\[ \begin{vmatrix} 240 & 198 \\ 219 & 181 \end{vmatrix} = (240 \cdot 181) - (198 \cdot 219) \]

Calculating this:

\[ = 43320 - 43482 = -162 \]

3. **Third determinant**:

\[ \begin{vmatrix} 240 & 225 \\ 219 & 198 \end{vmatrix} = (240 \cdot 198) - (225 \cdot 219) \]

Calculating this:

\[ = 47520 - 49375 = -1855 \]

### Step 3: Substitute back into the determinant equation

Now substitute the values of the 2x2 determinants back into the equation for \(D\):

\[ D = 265 \cdot 1521 - 240 \cdot (-162) + 219 \cdot (-1855) \]

Calculating each term:

1. \(265 \cdot 1521 = 403265\)
2. \(-240 \cdot (-162) = 38880\)
3. \(219 \cdot (-1855) = -406365\)

### Step 4: Combine the results

Now combine these results:

\[ D = 403265 + 38880 - 406365 \]

Calculating this gives:

\[ D = 403265 + 38880 - 406365 = 38880 \]

### Final Result

Thus, the value of the determinant is

\[ \boxed{38880} \]