Let's work out the expression \( p^4 - 49 \).

This expression is a **difference of squares**. The difference of squares formula states that:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In your expression:

- \( p^4 \) can be rewritten as \( (p^2)^2 \).
- \( 49 \) can be rewritten as \( 7^2 \).

So, applying the difference of squares formula:

\[
p^4 - 49 = (p^2)^2 - 7^2 = (p^2 - 7)(p^2 + 7)
\]

This is the factorized form of the expression.

So the fully worked out expression is:

\[
p^4 - 49 = (p^2 - 7)(p^2 + 7)
\]

Would you like a more detailed explanation or have any questions? 

Here are 5 related questions you might find useful:
1. How do you factorize higher degree polynomials?
2. What are the other types of special products?
3. How do you solve equations using the difference of squares?
4. Can the factorization of a difference of squares help in simplifying integrals?
5. What are the steps to factor completely a polynomial like \( p^6 - 64 \)?

**Tip:** When factorizing expressions, always check if they can be simplified by recognizing common patterns like the difference of squares, perfect square trinomials, or the sum/difference of cubes.

Learn how to factorize the expression p^4 - 49 using the difference of squares formula. This problem demonstrates key algebraic concepts such as factorization and the difference of squares theorem. Ideal for students in Grades 8-10.

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