Perfect Square Expansion: Complete (2x-?)² = 4x²-12x+?

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

• Step 1: Identify the given form and match it with the square of a difference formula
• Step 2: Determine the values of 'a' and 'b' such that the expanded form matches both sides of the equation
• Step 3: Calculate the missing value in the expression

Now, let's work through each step:
Step 1: We are given the expression $(2x-?)^2=4x^2-12x+\text{?}$.
Step 2: Using the standard formula for a perfect square expansion:
$(2x-b)^2 = (2x)^2 - 2 \cdot 2x \cdot b + b^2 = 4x^2 - 4xb + b^2$.
By matching coefficients, in $4x^2 - 12x + \text{?}$, we see $4xb = 12x$. Thus, $b = 3$.
Step 3: Substitute $b = 3$ into $b^2$ to get the constant term: $b^2 = 3^2 = 9$.

Therefore, the solution to the problem is $3,\text{ }9$.