To find the product \((v - 3)(v + 3)\), you can use the difference of squares formula, which states that:
\[ (a - b)(a + b) = a^2 - b^2 \]
In this case, \(a = v\) and \(b = 3\). Applying the formula:
\[ (v - 3)(v + 3) = v^2 - 3^2 = v^2 - 9 \]
Thus, the simplified answer is:
\[ \boxed{v^2 - 9} \]