https://r2.erweima.ai/mathbot/image/1725900495187vk8gqjie.jpg

The uploaded image contains a series of algebraic expressions asking for the factorization of each pair of terms using the difference of squares and the greatest common factor.

Let's start solving these equations step by step.

1. \( س^2 + 12س = س(س + 12) \)

2. \( س^2 - 49 = (س + 7)(س - 7) \)  
   (This is a difference of squares.)

3. \( 25ص^2 - 9 = (5ص + 3)(5ص - 3) \)  
   (Also a difference of squares.)

4. \( س^2 + 5س + 4 = (س + 4)(س + 1) \)  
   (This is factored by finding two numbers that multiply to 4 and add to 5.)

5. \( ص^2 + 6ص + 9 = (ص + 3)^2 \)  
   (This is a perfect square trinomial.)

6. \( س^2 + ص^2 = \text{Cannot be factored over real numbers.} \)

7. \( (س - ص)^2 = (س - ص)(س - ص) \)  
   (This is a square of a binomial.)

8. \( 25ل^2 - 1 = (5ل + 1)(5ل - 1) \)  
   (Another difference of squares.)

9. \( 49 + س = \text{Cannot be factored.} \)

10. \( س^2 - 25 = (س + 5)(س - 5) \)  
    (This is a difference of squares.)

11. \( 25س^2 - 16 = (5س + 4)(5س - 4) \)  
    (Another difference of squares.)

12. \( س^8ص^2 - س^2ص = س^2ص(س^6ص - 1) \)

Let me know if you want detailed explanations or if you have any questions. 

Here are 5 related questions to deepen your understanding:

1. How do you factor a perfect square trinomial?
2. What is the general formula for factoring the difference of squares?
3. Can the sum of squares be factored using real numbers?
4. How do you recognize when to use factoring by grouping?
5. What does it mean if an expression cannot be factored?

**Tip:** Always look for a greatest common factor (GCF) before attempting other factoring methods!

The image contains a series of algebraic expressions that require factorization using the difference of squares and finding the greatest common factor (GCF).

Learn how to factor algebraic expressions by using the difference of squares and finding the greatest common factor (GCF). This problem is suitable for students in Grades 8-10, covering key concepts in algebra including factoring trinomials, difference of squares, and GCF.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation