Factoring the difference of two squares that is the title of a video, I'm watching, the expression is 16(x-y)² -9 which my teacher work it out like this, 16(x-y)² -9 = 4²(x-y)² - 3² = [4(x-y)]² - 3² = [4(x-y) + 3] [4(x-y) - 3], I did it different is this correct 16(x-y)² -9 = 4²(x-y)² - 3² = 4²(x+y)(x-y) - 3² = (4+3)(4-3)(x+y)(x-y) is this correct?

Let's analyze both approaches to ensure clarity. 

### Expression to factor: 
\[
16(x-y)^2 - 9
\]

Your teacher's method proceeds as follows:

1. **Step 1:** Recognize that this is a difference of squares:
   \[
   16(x-y)^2 - 9 = (4(x-y))^2 - 3^2
   \]
   
2. **Step 2:** Apply the difference of squares formula:  
   \[
   a^2 - b^2 = (a+b)(a-b)
   \]
   So, 
   \[
   (4(x-y))^2 - 3^2 = [4(x-y) + 3][4(x-y) - 3]
   \]

Your teacher's solution is correct, and the factorization is:
\[
[4(x-y) + 3][4(x-y) - 3]
\]

### Now, let's check your method:
You wrote:

1. **Step 1:**  
   \[
   16(x-y)^2 - 9 = 4^2(x-y)^2 - 3^2
   \]
   This step is fine, as you are recognizing that both terms are squares.
   
2. **Step 2:**  
   \[
   4^2(x+y)(x-y) - 3^2
   \]
   This step is incorrect because you are factoring \( (x-y)^2 \) as \( (x+y)(x-y) \), which is not valid. The expression \( (x-y)^2 \) should remain as \( (x-y)(x-y) \), or \( (x-y)^2 \), without turning into a sum or difference of terms.

Thus, your approach contains an error. 

### Correct Conclusion:
Your teacher's solution is the correct factorization:
\[
16(x-y)^2 - 9 = [4(x-y) + 3][4(x-y) - 3]
\]
Your method deviated because you incorrectly factored \( (x-y)^2 \).

Would you like a further breakdown or practice on factoring? Here are some related questions:

1. Can you factor \( 25x^2 - 36 \)?
2. What is the factorization of \( 9a^2 - 1 \)?
3. How would you factor \( 49y^2 - 64 \)?
4. Factor \( 81z^2 - 4 \).
5. What is the factored form of \( 4m^2 - 25 \)?

**Tip:** Always be cautious when factoring expressions involving powers, and remember that only perfect squares can be factored using the difference of squares formula.

Factoring the difference of two squares that is the title of a video, I'm watching, the expression is 16(x-y)² -9 which my teacher worked out like this, 16(x-y)² -9 = 4²(x-y)² - 3² = [4(x-y)]² - 3² = [4(x-y) + 3] [4(x-y) - 3], I did it differently is this correct 16(x-y)² -9 = 4²(x-y)² - 3² = 4²(x+y)(x-y) - 3² = (4+3)(4-3)(x+y)(x-y) is this correct?

Explore how to factor the difference of squares in the expression 16(x-y)² - 9 with step-by-step guidance. This algebraic problem uses the difference of squares formula and is ideal for students in Grades 9-10.

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