The given expression is:

\[
9x^2 - 12x + 4
\]

To determine if it's a perfect square trinomial, let's check if it can be factored into the square of a binomial. A perfect square trinomial takes the form:

\[
(a x + b)^2 = a^2 x^2 + 2ab x + b^2
\]

For the trinomial \( 9x^2 - 12x + 4 \):

1. The first term \( 9x^2 \) is a perfect square: \( 9x^2 = (3x)^2 \), so \( a = 3 \).
2. The last term \( 4 \) is a perfect square: \( 4 = 2^2 \), so \( b = 2 \).
3. The middle term should be \( 2ab \). Let's check: \( 2(3)(2) = 12 \). Since the middle term is \(-12x\), we need a negative sign in the binomial.

Therefore, the expression can be written as:

\[
(3x - 2)^2
\]

Thus, the trinomial \( 9x^2 - 12x + 4 \) is a perfect square trinomial, and it factors as:

\[
(3x - 2)^2
\]

Would you like more details on this process, or do you have any questions?

Here are 5 related questions to explore:
1. What are the steps to factor a non-perfect square trinomial?
2. How can you recognize a perfect square trinomial by inspection?
3. What is the difference between factoring and completing the square?
4. Can you factor other types of trinomials without using squares?
5. How do you solve equations that contain perfect square trinomials?

**Tip**: To check if a trinomial is a perfect square, verify if the middle term is twice the product of the square roots of the first and last terms!

Learn how to factor the trinomial 9x² - 12x + 4 by recognizing it as a perfect square. This step-by-step solution explains key algebra concepts, including how to apply the perfect square trinomial formula. Ideal for students in Grades 8-10.

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