The expression to simplify is $(2x - 4)^2$.

Step-by-step simplification:

We use the formula for squaring a binomial: $(a - b)^2 = a^2 - 2ab + b^2$

Here, $a = 2x$ and $b = 4$. Substituting:

$(2x - 4)^2 = (2x)^2 - 2(2x)(4) + 4^2$

1. $(2x)^2 = 4x^2$
2. $-2(2x)(4) = -16x$
3. $4^2 = 16$

Now, combining the terms:

$(2x - 4)^2 = 4x^2 - 16x + 16$

Final Answer:

$4x^2 - 16x + 16$

Let me know if you'd like further clarification or have additional questions!

Here are 5 related questions for further exploration:

1. How do you expand $(3x + 5)^2$ using the same method?
2. What happens when $(2x - 4)^3$ is expanded?
3. How can the factoring method reverse this expansion?
4. Can you apply this method for $(ax + b)^2$ in a generalized way?
5. What is the graphical representation of $y = 4x^2 - 16x + 16$?

Tip: Always double-check your calculations by substituting simple values for $x$ to verify the expansion!