Find the products of the following by using the appropriate identity:
`(x-2)(x+3)`

Answer

To find the product of the expression \((x-2)(x+3)\) using an appropriate identity, we can use the identity for the product of two binomials:

\[ (a-b)(a+b) = a^2 - b^2 \]

However, in this case, we will use the general form for multiplying two binomials:

\[ (x + a)(x + b) = x^2 + (a + b)x + ab \]

### Step-by-Step Solution:

1. **Identify the values of \(a\) and \(b\)**:
- Here, we have \(a = -2\) (from \(x - 2\)) and \(b = 3\) (from \(x + 3\)).

2. **Apply the identity**:
- According to the identity, we can express the product as:
\[ (x - 2)(x + 3) = x^2 + (a + b)x + ab \]

3. **Calculate \(a + b\)**:
- Substitute \(a\) and \(b\):
\[ a + b = -2 + 3 = 1 \]

4. **Calculate \(ab\)**:
- Now calculate the product \(ab\):
\[ ab = (-2) \times 3 = -6 \]

5. **Substitute back into the identity**:
- Now we can substitute \(a + b\) and \(ab\) back into the identity:
\[ (x - 2)(x + 3) = x^2 + (1)x + (-6) \]

6. **Combine the terms**:
- This simplifies to:
\[ x^2 + x - 6 \]

### Final Answer:
Thus, the product of \((x - 2)(x + 3)\) is:
\[ x^2 + x - 6 \]