The expression \( p^4 - 256 \) can be factored using the difference of squares.

### Step-by-Step Factorization:
1. **Recognize the difference of squares**:  
   \( p^4 - 256 \) can be written as \( (p^2)^2 - (16)^2 \).

2. **Apply the difference of squares formula**:  
   The difference of squares formula is \( a^2 - b^2 = (a - b)(a + b) \).  
   Here, \( a = p^2 \) and \( b = 16 \).

   So,
   \[
   p^4 - 256 = (p^2 - 16)(p^2 + 16)
   \]

3. **Factor \( p^2 - 16 \)** further**:  
   Notice that \( p^2 - 16 \) is itself a difference of squares:
   \[
   p^2 - 16 = (p - 4)(p + 4)
   \]

Thus, the fully factored form of the expression is:
\[
p^4 - 256 = (p - 4)(p + 4)(p^2 + 16)
\]

### Summary:
The fully factored expression is \( (p - 4)(p + 4)(p^2 + 16) \).

Would you like more details on any part of the factorization process? Here are some related questions:

1. What is the difference of squares, and how is it used in algebra?
2. Can the term \( p^2 + 16 \) be factored further?
3. How do you recognize patterns in algebraic expressions for easier factorization?
4. What are some common factorization techniques used in algebra?
5. How does factoring help solve polynomial equations?

**Tip:** When factoring, always check if the expression can be simplified further by looking for common patterns like the difference of squares or sum/difference of cubes.

Explore how to factor the expression p^4 - 256 using the difference of squares method. This step-by-step solution delves into algebraic concepts, including polynomial factorization and the difference of squares theorem, making it ideal for students in Grades 9-11.

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