\( 1 \leftarrow \left\lvert\, \begin{array}{l}\text { Find the product. } \\ -(2 x-2)^{2} \\ -(2 x-2)^{2}= \)\begin{tabular}{|c|}\( -4^{2}+8 x-4 \)\end{tabular} \\ \( \begin{array}{l}\text { (Simplify your answer.) }\end{array}\end{array}\right. \)

To find the product \( -(2x - 2)^2 \), we first expand \( (2x - 2)^2 \). Using the formula \( (a - b)^2 = a^2 - 2ab + b^2 \): \[ (2x - 2)^2 = (2x)^2 - 2(2x)(2) + (2)^2 = 4x^2 - 8x + 4 \] Now, we apply the negative sign: \[ -(2x - 2)^2 = - (4x^2 - 8x + 4) = -4x^2 + 8x - 4 \] So, the simplified product is: \[ -4x^2 + 8x - 4 \]