Find the product. $$ -(2 x-4)^{2} $$ $$ -(2 x-4)^{2}=\square $$ (Simplify your answer.

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UpStudy AI · Accepted Answer

We start with the expression:
$$
-(2x-4)^2
$$

**Step 1. Expand the square.**

Recall the formula:
$$
(a-b)^2 = a^2 - 2ab + b^2
$$
Here, $$ a = 2x $$ and $$ b = 4 $$. So:
$$
(2x-4)^2 = (2x)^2 - 2(2x)(4) + 4^2 = 4x^2 - 16x + 16
$$

**Step 2. Multiply the expanded expression by $$-1$$.**

$$
-(2x-4)^2 = -\Bigl(4x^2 - 16x + 16\Bigr) = -4x^2 + 16x - 16
$$

Thus, the simplified form is:
$$
-(2x-4)^2 = -4x^2 + 16x - 16
$$
$$-(2x-4)^2 = -4x^2 + 16x - 16$$

Find the product. \( -(2 x-4)^{2} \) \( -(2 x-4)^{2}=\square \) (Simplify your answer.

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