Completing the Polynomial: Fill in the Gap in 2x^2 - __ = 2(x-4)(x+4)

Fill in the missing element to obtain a true expression:

$2x^2-_{_—}=2(x-4)\cdot(x+4)$

To solve this problem, we'll follow these steps:

• Step 1: Expand the expression on the right side of the equation.
• Step 2: Compare it with the left-hand side equation and find the missing number.

Now, let's work through each step:
Step 1: Expand the expression $2(x-4)(x+4)$. Using the difference of squares, this becomes:

Step 2: Compare it with the original left side $2x^2 - \_ = 2x^2 - 32$.

The missing number must be 32 so that both sides of the equation are equal.

Therefore, the solution to the problem is $\textbf{32}$.