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The problem asks us to factor the trinomial \( 4x^2 - 8x + 4 \) in the form of \( (Ax - B)^2 \), where \( A \) and \( B \) are constants to be determined.

Let's start by recognizing that this is a perfect square trinomial. We want to express \( 4x^2 - 8x + 4 \) as the square of a binomial. Here’s how we approach this:

1. **Identify the coefficients:**
   - The first term is \( 4x^2 \), which is the square of \( 2x \), so \( A = 2 \).
   - The last term is \( 4 \), which is the square of \( 2 \), so \( B = 2 \).

2. **Check the middle term:**
   The middle term should be twice the product of \( A \) and \( B \), i.e., \( -2 \times A \times B \).
   \[
   -2 \times 2 \times 2 = -8x
   \]
   This matches the middle term in the original trinomial.

Therefore, we can factor the trinomial as:
\[
4x^2 - 8x + 4 = (2x - 2)^2
\]

Thus, \( A = 2 \) and \( B = 2 \).

### Final Answer:
- \( A = 2 \)
- \( B = 2 \)

Would you like more details on how perfect square trinomials are factored? Here are some related questions:

1. How do you identify a perfect square trinomial?
2. Can this technique be applied to any trinomial?
3. What happens if the middle term doesn't match twice the product of \( A \) and \( B \)?
4. How do you check if a trinomial is factored correctly?
5. Can we factor this trinomial in other ways besides a perfect square?

**Tip:** Always verify the middle term when factoring perfect square trinomials to avoid errors.

Factor the trinomial 4x^2 - 8x + 4 and find the values of A and B in the form (Ax - B)^2.

Learn how to factor the perfect square trinomial 4x^2 - 8x + 4. This solution guides you through identifying key components and applying the factoring formula for trinomials. Perfect for students in Grades 8-10.

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