The given expression is:

\[
x^2 - 6x + 9
\]

Let's analyze it:

### Step 1: Recognize the form
This expression is a quadratic expression. Notice that it resembles a perfect square trinomial, which follows the form:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]

In this case, we can rewrite:
\[
x^2 - 6x + 9 = (x - 3)^2
\]

### Step 2: Confirm by expanding
To confirm that \( (x - 3)^2 \) is correct, let's expand it:
\[
(x - 3)^2 = (x - 3)(x - 3)
\]
\[
= x^2 - 3x - 3x + 9
\]
\[
= x^2 - 6x + 9
\]
Since the expanded form matches the original expression, we can conclude:

\[
x^2 - 6x + 9 = (x - 3)^2
\]

### Final Answer:
The expression \(x^2 - 6x + 9\) is equivalent to \((x - 3)^2\).

Would you like more details or have any further questions?

Here are 5 related questions:
1. What is a perfect square trinomial?
2. How do you factor quadratic expressions that are not perfect squares?
3. How do you solve \(x^2 - 6x + 9 = 0\)?
4. What is the difference between factoring and expanding expressions?
5. Can every quadratic expression be factored?

**Tip:** Recognizing perfect square trinomials can simplify solving quadratic equations or factoring expressions quickly!

Learn how to factor the quadratic expression x^2 - 6x + 9 as a perfect square trinomial. This problem involves key algebraic concepts, such as recognizing and factoring perfect squares. Detailed step-by-step explanation for Grades 8-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation