`(3-sqrt7)(3+sqrt7)=?`

Answer

To solve the expression \((3 - \sqrt{7})(3 + \sqrt{7})\), we can use the algebraic identity for the difference of squares. The identity states that:

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

### Step-by-step Solution:

1. **Identify \(a\) and \(b\)**:
- Here, we can identify \(a = 3\) and \(b = \sqrt{7}\).

2. **Apply the difference of squares identity**:
- Using the identity, we can rewrite the expression:
\[ (3 - \sqrt{7})(3 + \sqrt{7}) = a^2 - b^2 \]

3. **Calculate \(a^2\)**:
- Calculate \(3^2\):
\[ 3^2 = 9 \]

4. **Calculate \(b^2\)**:
- Calculate \((\sqrt{7})^2\):
\[ (\sqrt{7})^2 = 7 \]

5. **Substitute \(a^2\) and \(b^2\) into the identity**:
- Now substitute the values back into the equation:
\[ 9 - 7 \]

6. **Perform the subtraction**:
- Finally, calculate:
\[ 9 - 7 = 2 \]

### Final Answer:
Thus, the value of \((3 - \sqrt{7})(3 + \sqrt{7})\) is \(2\).

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