https://file.aiquickdraw.com/mathbot/file/1726588309029szcwxv1p.jpg

Let's match each expression with its correct factored form from the image.

1. **\( 4x^2 + 8x \)**  
   This can be factored by taking out the greatest common factor (GCF), which is \( 4x \).  
   Factored form: \( 4x(x + 2) \)  
   **Match**: **b**. \( 4x(x + 2) \)

2. **\( 9x^2 - 4 \)**  
   This is a difference of squares, as \( 9x^2 = (3x)^2 \) and \( 4 = 2^2 \).  
   Factored form: \( (3x + 2)(3x - 2) \)  
   **Match**: **d**. \( (3x + 2)(3x - 2) \)

3. **\( x^2 - 16 \)**  
   This is also a difference of squares, as \( x^2 = (x)^2 \) and \( 16 = 4^2 \).  
   Factored form: \( (x + 4)(x - 4) \)  
   **Match**: **a**. \( (x + 4)(x - 4) \)

4. **\( x^2 - x - 6 \)**  
   This is a trinomial that can be factored by finding two numbers that multiply to \( -6 \) and add to \( -1 \), which are \( -3 \) and \( 2 \).  
   Factored form: \( (x - 3)(x + 2) \)  
   **Match**: **c**. \( (x - 3)(x + 2) \)

### Final matches:
- \( 4x^2 + 8x \) → **b**. \( 4x(x + 2) \)
- \( 9x^2 - 4 \) → **d**. \( (3x + 2)(3x - 2) \)
- \( x^2 - 16 \) → **a**. \( (x + 4)(x - 4) \)
- \( x^2 - x - 6 \) → **c**. \( (x - 3)(x + 2) \)

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Do you need further clarification on any of these factorizations? 

Here are five related questions you might find interesting:
1. How do you factor a general quadratic equation \( ax^2 + bx + c \)?
2. What is the difference between factoring by grouping and factoring using the quadratic formula?
3. Can all quadratics be factored, or are there cases where factoring is impossible?
4. How do you recognize a difference of squares when factoring?
5. Why is factoring an important skill for solving algebraic equations?

**Tip**: Always check your factorization by expanding it back to its original form to ensure it's correct!

Match each expression with the correct factored form.

Learn how to factor algebraic expressions such as quadratics, difference of squares, and trinomials. This guide provides step-by-step solutions for factoring expressions like 4x^2 + 8x, 9x^2 - 4, x^2 - 16, and x^2 - x - 6. Suitable for Grades 7-10.

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