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.