Express the product \( (2+\sqrt{7})(2-\sqrt{7}) \) in simplest form.

To express the product \( (2+\sqrt{7})(2-\sqrt{7}) \) in simplest form, we can use the difference of squares formula, which states that \( (a+b)(a-b) = a^2 - b^2 \). Here, let \( a = 2 \) and \( b = \sqrt{7} \). So, we have: \[ (2+\sqrt{7})(2-\sqrt{7}) = 2^2 - (\sqrt{7})^2 \] Calculating these squares gives us: \[ 2^2 = 4 \quad \text{and} \quad (\sqrt{7})^2 = 7 \] Substituting these values back into the equation: \[ (2+\sqrt{7})(2-\sqrt{7}) = 4 - 7 \] Now, simplifying this results in: \[ 4 - 7 = -3 \] Thus, the product \( (2+\sqrt{7})(2-\sqrt{7}) \) in simplest form is \[ \boxed{-3} \]