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The expression you provided is:

\[
(x^2 + 7)(x^2 - 7)
\]

This is a difference of squares, which follows the identity:

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

In this case, \(a = x^2\) and \(b = 7\). Applying the identity:

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

Thus, the simplified expression is:

\[
x^4 - 49
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:

1. How would you solve \( (x^2 + 5)(x^2 - 5) \)?
2. Can the difference of squares method be applied to \( (x^3 + 9)(x^3 - 9) \)? Why or why not?
3. What happens if you have an expression like \( (x^2 + 7)(x^2 + 7) \)? How is this different from the given problem?
4. How do you factor an expression like \( x^4 - 49 \)?
5. What is the general form of the difference of squares formula?

**Tip:** The difference of squares identity is a very useful tool in algebra to simplify expressions and solve equations quickly.

Learn how to simplify the algebraic expression (x^2 + 7)(x^2 - 7) using the Difference of Squares formula. This concept is commonly taught in Grades 8-10 and helps students solve quadratic expressions efficiently.

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