## Factoring the Expression (n+2)(n-2)

The expression (n+2)(n-2) is a classic example of the **difference of squares** pattern. This pattern arises when we have two binomials, one with addition and one with subtraction, where both binomials share the same terms.

### Understanding the Difference of Squares

The difference of squares pattern states that:

**(a + b)(a - b) = a² - b²**

In our case, **a = n** and **b = 2**. Applying the pattern, we can expand the expression:

(n + 2)(n - 2) = n² - 2²

### Simplifying the Expression

Simplifying the expression further, we get:

**n² - 2² = n² - 4**

Therefore, the factored form of (n + 2)(n - 2) is **n² - 4**.

### Applications of the Difference of Squares

The difference of squares pattern is frequently used in algebra and other mathematical fields. Here are some examples of its applications:

**Factoring polynomials:**It allows us to simplify complex expressions and make further calculations easier.**Solving equations:**By recognizing the pattern, we can quickly solve equations that involve the difference of squares.**Trigonometry:**The pattern is applied in trigonometric identities and formulas.

### Conclusion

The expression (n+2)(n-2) can be factored using the difference of squares pattern, resulting in the simplified expression n² - 4. This pattern has wide applications in mathematics, making it a fundamental concept to understand.