(n-2).jpeg "(n+2)(n-2)")
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.