Expand ` |(8x, 3), (2, 2)|`

Answer

To expand the determinant \( |(8x, 3), (2, 2)| \), we can follow these steps:

### Step 1: Set up the determinant
We denote the determinant as \( \Delta \):
\[ \Delta = |(8x, 3), (2, 2)| \]

### Step 2: Apply the formula for 2x2 determinants
For a 2x2 determinant of the form:
\[ | (a, b), (c, d) | = ad - bc \]
we can substitute \( a = 8x \), \( b = 3 \), \( c = 2 \), and \( d = 2 \).

### Step 3: Substitute the values into the formula
Now, we substitute the values into the determinant formula:
\[ \Delta = (8x \cdot 2) - (3 \cdot 2) \]

### Step 4: Calculate the products
Calculating the products gives us:
\[ \Delta = 16x - 6 \]

### Step 5: Final result
Thus, the expanded form of the determinant is:
\[ \Delta = 16x - 6 \]