►𝑥
2 + 8𝑥 + 16
►𝑥
2 − 6𝑥 + 9

The expressions you've provided look like quadratic expressions. Let's rewrite and analyze them:

1. \( x^2 + 8x + 16 \)
2. \( x^2 - 6x + 9 \)

### 1. Factoring \( x^2 + 8x + 16 \)
The first expression is a perfect square trinomial:
\[
x^2 + 8x + 16 = (x + 4)(x + 4) = (x + 4)^2
\]
This is because \( 4^2 = 16 \) and \( 2 \cdot 4 \cdot x = 8x \).

### 2. Factoring \( x^2 - 6x + 9 \)
Similarly, the second expression is also a perfect square trinomial:
\[
x^2 - 6x + 9 = (x - 3)(x - 3) = (x - 3)^2
\]
This is because \( (-3)^2 = 9 \) and \( 2 \cdot (-3) \cdot x = -6x \).

### Summary:
- \( x^2 + 8x + 16 = (x + 4)^2 \)
- \( x^2 - 6x + 9 = (x - 3)^2 \)

These are both quadratic expressions factored into their respective squares.

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

Here are some related questions:
1. How can I solve quadratic equations using the quadratic formula?
2. What does it mean when a quadratic expression is a perfect square trinomial?
3. How can I complete the square to factor non-perfect square trinomials?
4. What are the properties of quadratic functions in vertex form?
5. How can I graph the functions \( y = (x + 4)^2 \) and \( y = (x - 3)^2 \)?

**Tip:** Factoring perfect square trinomials can simplify solving quadratic equations, as their factored form reveals repeated roots.

Learn how to factor perfect square trinomials like x^2 + 8x + 16 and x^2 - 6x + 9. This step-by-step guide covers key algebraic concepts, including factoring and identifying perfect square trinomials, ideal for Grades 8-10.

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