https://file.aiquickdraw.com/mathbot/file/17281024482191iuvqebz.jpg

The expression in the image is:

\[
36x^2 - 108x + 81
\]

This is a quadratic expression, and it looks like it might be factorable. Let's attempt to factor it.

### Step-by-Step Factorization:

1. First, note that all the coefficients are divisible by 9. So, we can factor out 9:

\[
36x^2 - 108x + 81 = 9(4x^2 - 12x + 9)
\]

2. Now, let's try to factor the quadratic inside the parentheses:

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

This is a perfect square trinomial because the first term is \((2x)^2\), the last term is \(3^2\), and the middle term is twice the product of 2x and 3. So it factors as:

\[
4x^2 - 12x + 9 = (2x - 3)^2
\]

3. Therefore, the original expression can be factored as:

\[
36x^2 - 108x + 81 = 9(2x - 3)^2
\]

So, the factored form of the expression is:

\[
9(2x - 3)^2
\]

Would you like further details or have any questions?

---

Here are 5 questions to expand your understanding:
1. What is a perfect square trinomial, and how can you identify one?
2. How would you solve the equation \(36x^2 - 108x + 81 = 0\) using this factorization?
3. What other methods could be used to factor a quadratic if it is not a perfect square?
4. How does factoring help in solving quadratic equations?
5. Can you verify the factorization by expanding \(9(2x - 3)^2\) back into its original form?

**Tip:** Always check for common factors before attempting more complex factoring techniques!

Learn how to factor the quadratic expression 36x^2 - 108x + 81 by recognizing it as a perfect square trinomial. This step-by-step guide explains key algebraic concepts such as factorization, common factors, and the perfect square trinomial theorem. Suitable for students in Grades 8-10.

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