Multiply. \[ [x-(6+2 i)][x-(6-2 i)] \] Note that these expressions contain complex numbers. Simplify your answer as much as possible.

To multiply the given expressions \( [x - (6 + 2i)][x - (6 - 2i)] \), we can first expand using the distributive property. Let \( a = x - (6 + 2i) \) and \( b = x - (6 - 2i) \). Thus, we have: \[ ab = (x - 6 - 2i)(x - 6 + 2i) \] This expression represents the product of a complex number and its conjugate. We can use the difference of squares formula, \( (a - b)(a + b) = a^2 - b^2 \), with \( a = x - 6 \) and \( b = 2i \): \[ (x - 6)^2 - (2i)^2 \] Calculating \( (2i)^2 \): \[ (2i)^2 = 4i^2 = 4(-1) = -4 \] Now, substituting this back into the expression: \[ (x - 6)^2 - (-4) = (x - 6)^2 + 4 \] Next, we expand \( (x - 6)^2 \): \[ (x - 6)^2 = x^2 - 12x + 36 \] Adding the 4 gives: \[ x^2 - 12x + 36 + 4 = x^2 - 12x + 40 \] Thus, the simplified result is: \[ \boxed{x^2 - 12x + 40} \]