Let's solve the problem in the image:

We need to factor the expression $4x^2 - 4$.

Step 1: Factor out the greatest common factor (GCF)

The GCF of $4x^2$ and $-4$ is $4$. Factoring it out: $4x^2 - 4 = 4(x^2 - 1)$

Step 2: Factor the remaining quadratic

The term $x^2 - 1$ is a difference of squares, which factors as: $x^2 - 1 = (x - 1)(x + 1)$

Final Factored Form:

$4x^2 - 4 = 4(x - 1)(x + 1)$

Correct Answer:

The correct option is d) $4(x - 1)(x + 1)$.

Do you want further details or have questions about this?
Here are 5 related questions to deepen your understanding:

1. How do you identify and factor a difference of squares?
2. What is the importance of factoring out the greatest common factor first?
3. Can $x^2 + 1$ be factored over the real numbers? Why or why not?
4. How does factoring help simplify expressions in equations?
5. What are some examples of real-world applications of factoring?

Tip: Always check for a common factor before applying other factoring methods!