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The worksheet asks to factor each polynomial, and then check the answer using FOIL. Let's go through the problems one by one, recognizing patterns like **difference of squares** and **perfect square trinomials**.

### 1. \( x^2 - 36 \)
This is a difference of squares:  
\[
x^2 - 36 = (x - 6)(x + 6)
\]

### 2. \( a^2b^2 - 100 \)
This is also a difference of squares:
\[
a^2b^2 - 100 = (ab - 10)(ab + 10)
\]

### 3. \( 16y^2 - 25 \)
This is a difference of squares:
\[
16y^2 - 25 = (4y - 5)(4y + 5)
\]

### 4. \( y^2 + 49 \)
This is **not** factorable using real numbers, as it is a sum of squares.

### 5. \( 9a^2 - 121 \)
This is a difference of squares:
\[
9a^2 - 121 = (3a - 11)(3a + 11)
\]

### 6. \( 196 - x^2 \)
This is a difference of squares:
\[
196 - x^2 = (14 - x)(14 + x)
\]

### 7. \( 4y^2 - 81 \)
This is a difference of squares:
\[
4y^2 - 81 = (2y - 9)(2y + 9)
\]

### 8. \( 36c^2 - d^2 \)
This is a difference of squares:
\[
36c^2 - d^2 = (6c - d)(6c + d)
\]

### 9. \( 16m^2 - p^2 \)
This is a difference of squares:
\[
16m^2 - p^2 = (4m - p)(4m + p)
\]

### 10. \( m^2 - 64n^2 \)
This is a difference of squares:
\[
m^2 - 64n^2 = (m - 8n)(m + 8n)
\]

### 11. \( 1 - 4a^2 \)
This is a difference of squares:
\[
1 - 4a^2 = (1 - 2a)(1 + 2a)
\]

### 12. \( 9v^4 - 100 \)
This is a difference of squares:
\[
9v^4 - 100 = (3v^2 - 10)(3v^2 + 10)
\]

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Let me know if you need further clarification or want me to explain any specific step! Here are some related questions for more practice:

1. How would you apply the FOIL method to verify the factoring of \( x^2 - 36 \)?
2. Can you recognize which polynomials are **sum of squares** and why they are not factorable over the real numbers?
3. How does recognizing the pattern of a difference of squares help in factoring complex expressions?
4. What is the geometric interpretation of a difference of squares?
5. How would you factor a trinomial like \( x^2 + 6x + 9 \)?

**Tip:** For difference of squares, always look for two perfect squares being subtracted!

Factor each polynomial, if possible. Check your answer using FOIL.

Learn how to factor polynomials using the difference of squares method. This worksheet includes examples like x^2 - 36, a^2b^2 - 100, and others. Suitable for students in Grades 8-10.

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