To find an equivalent expression for [tex]\((2x-4)(2x+4)(2x+4)(2x+4)'\)[/tex], let's simplify the given expression step-by-step:
1. Identify and group the repeated terms:
[tex]\[
(2x-4)(2x+4)(2x+4)(2x+4)^{\prime}
\][/tex]
2. Notice that the term [tex]\((2x+4)\)[/tex] is repeated three times. Therefore, we can rewrite the expression to show this repetition more clearly:
[tex]\[
(2x-4)(2x+4)^3
\][/tex]
According to our simplified expression, [tex]\((2x-4)(2x+4)^3\)[/tex] is the equivalent form.
Therefore, the correct choice from the given options is:
[tex]\[
(2 x-4)(2 x+4)^3
\][/tex]
This matches the first option provided. So, the final answer is:
[tex]\[
(2 x-4)(2 x+4)^3
\][/tex]
