To factorize the expression \(4a^2 - 49\), we recognize that it is a difference of squares. The difference of squares formula is given by:

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

In this case, \(4a^2\) and \(49\) are both perfect squares:
- \(4a^2 = (2a)^2\)
- \(49 = 7^2\)

So, we can rewrite the expression as:

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

Applying the difference of squares formula:

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

Therefore, the factorized form of \(4a^2 - 49\) is:

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

Would you like more details or have any questions?

Here are 8 related questions for further exploration:
1. How do you factorize \(x^2 - 25\)?
2. What is the factored form of \(9a^2 - 16\)?
3. How do you recognize a difference of squares?
4. Can you factorize \(25b^2 - 36c^2\)?
5. What is the factored form of \(a^4 - b^4\)?
6. How do you factorize \(x^2 - y^2\)?
7. What is the significance of recognizing perfect squares in factorization?
8. How do you solve \(4a^2 - 49 = 0\)?

**Tip:** When factorizing polynomials, always check for common patterns such as the difference of squares, perfect square trinomials, and the sum or difference of cubes.

Learn how to factorize the expression 4a^2 - 49 using the difference of squares formula. This problem involves recognizing perfect squares and applying mathematical theorems to simplify the expression. Suitable for high school students.

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