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The given trinomial is \( 4x^2 - 20x + 25 \), and we are asked to express it as a perfect square trinomial in the form \( (Ax - B)^2 \).

### Step 1: Recognize the general form of a perfect square trinomial
A perfect square trinomial takes the form:
\[
(Ax - B)^2 = A^2x^2 - 2ABx + B^2
\]
We will compare this form with the given trinomial \( 4x^2 - 20x + 25 \).

### Step 2: Match the coefficients
- The term \( A^2x^2 \) corresponds to \( 4x^2 \). This gives us \( A^2 = 4 \), so \( A = 2 \).
- The constant term \( B^2 \) corresponds to \( 25 \). This gives us \( B^2 = 25 \), so \( B = 5 \).
- Now, let's verify with the middle term:
  \[
  -2ABx = -2(2)(5)x = -20x
  \]
  This matches the middle term of the given trinomial.

### Step 3: Conclusion
Thus, \( 4x^2 - 20x + 25 \) can be written as:
\[
(2x - 5)^2
\]

### Final Answer:
\[
( \boxed{2} x - \boxed{5} )^2
\]

Would you like further details or have any questions?

Here are some related questions you might consider:
1. How do we identify perfect square trinomials?
2. What happens if the trinomial doesn't exactly match a perfect square form?
3. Can a perfect square trinomial ever have a positive middle term?
4. How would you complete the square for a general quadratic trinomial?
5. What are some practical applications of perfect square trinomials?

**Tip:** When factoring perfect square trinomials, always check if the middle term matches \( 2ABx \) to ensure the factorization is correct!

The trinomial 4x^2 - 20x + 25 is a perfect square trinomial. That is, 4x^2 - 20x + 25 = (Ax - B)^2 for some A and B. Fill in the boxes below with the two numbers.

Learn how to factor the perfect square trinomial 4x^2 - 20x + 25. This detailed solution guides you through recognizing and solving perfect square trinomials using the formula (Ax - B)^2. Suitable for high school algebra students.

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