Multiply using the rule for the product of the sum and difference of two terms. \[ \begin{array}{l}(x-6)(x+6) \\ (x-6)(x+6)=\square\end{array} \]

To multiply the expression \((x-6)(x+6)\) using the rule for the product of the sum and difference of two terms, we can use the identity: \[ (a-b)(a+b) = a^2 - b^2 \] In this case, we can identify \(a = x\) and \(b = 6\). Therefore, we can apply the identity as follows: \[ (x-6)(x+6) = x^2 - 6^2 \] Now, we calculate \(6^2\): \[ 6^2 = 36 \] Substituting this back into the equation gives us: \[ (x-6)(x+6) = x^2 - 36 \] Thus, the final result is: \[ (x-6)(x+6) = x^2 - 36 \] So, we fill in the square: \[ (x-6)(x+6) = x^2 - 36 \]