If `Delta` is an operation such that for integers a and b we have `a Deltab=axxa+bxxb-axxb`, then find `(-3) Delta` 2.

Answer

To solve the problem using the operation defined as \( a \Delta b = a \times a + b \times b - a \times b \), we need to find the value of \( (-3) \Delta 2 \).

### Step-by-Step Solution:

1. **Substitute the values into the operation**:
We have \( a = -3 \) and \( b = 2 \). So, we substitute these values into the operation:
\[ (-3) \Delta 2 = (-3) \times (-3) + 2 \times 2 - (-3) \times 2 \]

2. **Calculate each term**:
- First, calculate \( (-3) \times (-3) \):
\[ (-3) \times (-3) = 9 \]
- Next, calculate \( 2 \times 2 \):
\[ 2 \times 2 = 4 \]
- Finally, calculate \( -(-3) \times 2 \):
\[ -(-3) \times 2 = 3 \times 2 = 6 \]

3. **Combine the results**:
Now, we combine all the calculated terms:
\[ 9 + 4 - 6 \]

4. **Perform the addition and subtraction**:
- First, add \( 9 + 4 \):
\[ 9 + 4 = 13 \]
- Then, subtract \( 6 \) from \( 13 \):
\[ 13 - 6 = 7 \]

5. **Final Result**:
Therefore, the value of \( (-3) \Delta 2 \) is:
\[ (-3) \Delta 2 = 7 \]