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This worksheet is about factoring expressions, and it appears to create a word puzzle (the "GridWord") from the factored terms. Let's begin by factoring each expression. I'll go step by step for each one.

### 1. \( 16a^4 - 9 \)
This is a difference of squares:
\[
16a^4 - 9 = (4a^2 - 3)(4a^2 + 3)
\]

### 2. \( b^2 - a^6 \)
Also a difference of squares:
\[
b^2 - a^6 = (b - a^3)(b + a^3)
\]

### 3. \( 25x^2 - 4y^2 \)
Again, a difference of squares:
\[
25x^2 - 4y^2 = (5x - 2y)(5x + 2y)
\]

### 4. \( x^4 - 1 \)
Another difference of squares:
\[
x^4 - 1 = (x^2 - 1)(x^2 + 1)
\]
Then, factor \( x^2 - 1 \) further as:
\[
x^4 - 1 = (x - 1)(x + 1)(x^2 + 1)
\]

### 5. \( 36a^8 - b^6 \)
This is also a difference of squares:
\[
36a^8 - b^6 = (6a^4 - b^3)(6a^4 + b^3)
\]

### 6. \( x^4 - y^4 \)
Another difference of squares:
\[
x^4 - y^4 = (x^2 - y^2)(x^2 + y^2)
\]
Then, factor \( x^2 - y^2 \) further:
\[
x^4 - y^4 = (x - y)(x + y)(x^2 + y^2)
\]

### 7. \( 4y - 1 \)
This is already factored:
\[
4y - 1
\]

### 8. \( a^2 - 9b^4 \)
Difference of squares:
\[
a^2 - 9b^4 = (a - 3b^2)(a + 3b^2)
\]

### 9. \( x^{12} - 36 \)
Factor the constants first:
\[
x^{12} - 36 = (x^6 - 6)(x^6 + 6)
\]
\( x^6 - 6 \) cannot be factored further, so this is the final form.

### 10. \( 9a^2 - 1 \)
Another difference of squares:
\[
9a^2 - 1 = (3a - 1)(3a + 1)
\]

### 11. \( a^{12} - 16 \)
Factor as a difference of squares:
\[
a^{12} - 16 = (a^6 - 4)(a^6 + 4)
\]
Then factor \( a^6 - 4 \) further:
\[
a^{12} - 16 = (a^3 - 2)(a^3 + 2)(a^6 + 4)
\]

### 12. \( 4y^4 - 9 \)
Difference of squares:
\[
4y^4 - 9 = (2y^2 - 3)(2y^2 + 3)
\]

### 13. \( x^6 - a^2 \)
Difference of squares:
\[
x^6 - a^2 = (x^3 - a)(x^3 + a)
\]

### 14. \( y^2 - 64 \)
Difference of squares:
\[
y^2 - 64 = (y - 8)(y + 8)
\]

### 15. \( 4b^2 - 9 \)
Difference of squares:
\[
4b^2 - 9 = (2b - 3)(2b + 3)
\]

### 16. \( 25a^8 - b^2 \)
Difference of squares:
\[
25a^8 - b^2 = (5a^4 - b)(5a^4 + b)
\]

### 17. \( 16y^4 - 1 \)
Difference of squares:
\[
16y^4 - 1 = (4y^2 - 1)(4y^2 + 1)
\]
Factor \( 4y^2 - 1 \) further:
\[
16y^4 - 1 = (2y - 1)(2y + 1)(4y^2 + 1)
\]

### 18. \( 49x^2 - 9 \)
Difference of squares:
\[
49x^2 - 9 = (7x - 3)(7x + 3)
\]

### 19. \( y^6 - b^2 \)
Difference of squares:
\[
y^6 - b^2 = (y^3 - b)(y^3 + b)
\]

### 20. \( 9b^{10} - 1 \)
Difference of squares:
\[
9b^{10} - 1 = (3b^5 - 1)(3b^5 + 1)
\]

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Let me know if you'd like me to work through the puzzle for the "GridWord" or explain any step further! 

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**Questions for further exploration:**
1. Can you explain how the difference of squares is applied to factor polynomials?
2. How can I factor expressions that aren't difference of squares?
3. What do you do when an expression involves more complex exponents, like \(x^6\)?
4. How do you handle expressions that don't simplify easily, like prime polynomials?
5. What happens when factoring leads to terms that can't be simplified further?

**Tip:** Always check if you can apply the difference of squares when you see subtraction between two terms involving even exponents!

Factoring algebraic expressions worksheet, including the difference of squares and similar factoring methods to form a grid word.

Solve factoring problems including difference of squares and higher-degree algebraic expressions. This worksheet provides a detailed step-by-step solution and explores key algebraic concepts suitable for Grades 9-12.

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