Expand [4(2-x)]²: Square Brackets and Binomial Expression

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

• Step 1: Simplify inside the bracket.
• Step 2: Apply the square of a binomial formula.
• Step 3: Expand and simplify the expression.

Now, let's work through each step:

Step 1: Simplify inside the bracket:
The expression inside the bracket is $4(2-x)$. Multiplying through by 4, we have:
$= 4 \times (2-x) = 8 - 4x$.

Step 2: Apply the square of a binomial formula:
We want to compute $(8 - 4x)^2$. According to the binomial formula:
$(a-b)^2 = a^2 - 2ab + b^2$.

Let $a = 8$ and $b = 4x$. Substituting these into the formula gives us:
$(8 - 4x)^2 = 8^2 - 2(8)(4x) + (4x)^2$.

Step 3: Expand and simplify the expression:
$= 64 - 64x + 16x^2$.

The correctly expanded expression is:
Therefore, the solution to the problem is $\mathbf{16x^2 - 64x + 64}$.