https://r2.erweima.ai/mathbot/image/1723751034338qri6bm2r.jpg

hacer cada uno de los ejercicios por factorizar

To solve each of these exercises by factoring, I'll begin by analyzing the image and identifying the expressions that need to be factored. I'll then provide step-by-step solutions for each.

### Analyzing the Image:

The image contains six algebraic expressions labeled from 13 to 18. I'll solve them by factoring.

---

### **Exercise 13:**
\[
x^2 + 2x + 1
\]

**Solution:**
This is a perfect square trinomial. It can be factored as:
\[
(x + 1)^2
\]

---

### **Exercise 14:**
\[
y^2 - 4
\]

**Solution:**
This is a difference of squares. It can be factored as:
\[
(y - 2)(y + 2)
\]

---

### **Exercise 15:**
\[
4x^2 - 12x + 9
\]

**Solution:**
This is a perfect square trinomial. It can be factored as:
\[
(2x - 3)^2
\]

---

### **Exercise 16:**
\[
x^2 + 6x + 9
\]

**Solution:**
This is a perfect square trinomial. It can be factored as:
\[
(x + 3)^2
\]

---

### **Exercise 17:**
\[
x^2 - 9
\]

**Solution:**
This is another difference of squares. It can be factored as:
\[
(x - 3)(x + 3)
\]

---

### **Exercise 18:**
\[
9x^2 - 12x + 4
\]

**Solution:**
This is also a perfect square trinomial. It can be factored as:
\[
(3x - 2)^2
\]

---

Each of these expressions has been factored using methods such as identifying perfect square trinomials and recognizing differences of squares. Let me know if you would like further details on any of the solutions or if you have additional questions!

### Questions:
1. How can you recognize a perfect square trinomial?
2. What are the steps to factor a difference of squares?
3. How would you factor a trinomial that is not a perfect square?
4. Can the quadratic formula be used as an alternative method for factoring?
5. What are common mistakes when factoring perfect squares?
6. How does factoring relate to solving quadratic equations?
7. What is the significance of the coefficients in recognizing factorable expressions?
8. How can you check if a factorization is correct?

**Tip:** Always look for common factors first before attempting more complex factoring methods. This can simplify the problem significantly.

Learn how to solve algebraic expressions by factoring with step-by-step solutions. This problem set covers factoring methods such as perfect square trinomials and difference of squares. Suitable for high school students studying algebra.

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