The difference of two squares is a common algebraic identity, which states:

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

In your case, the expression is \( 4x^2 - 49 \).

First, we can rewrite \( 4x^2 \) and \( 49 \) as squares:

\[
4x^2 = (2x)^2 \quad \text{and} \quad 49 = 7^2
\]

So, the expression \( 4x^2 - 49 \) can be factored as:

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

Using the difference of squares formula:

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

Thus, the factored form of \( 4x^2 - 49 \) is:

\[
\boxed{(2x - 7)(2x + 7)}
\]

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. How do you factor \(9x^2 - 25\) using the difference of squares?
2. Can the difference of two squares be applied to non-integer values?
3. What happens if \( a^2 - b^2 \) includes a negative or zero value for \( b^2 \)?
4. How do you solve \( (2x - 7)(2x + 7) = 0 \)?
5. What are some real-world applications of the difference of squares?

**Tip:** Always check if an expression can be factored by identifying perfect squares, which simplifies the equation and aids in solving it.

Learn how to factor the expression 4x^2 - 49 using the difference of squares formula with a detailed step-by-step solution. This problem covers key algebraic concepts, including the difference of squares, factoring, and quadratic equations. Suitable for students in Grades 9-12.

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