%5E2-(3n%2B2)%5E2.jpeg "(3n+4)^2-(3n+2)^2")
Simplifying the Expression (3n+4)^2 - (3n+2)^2
This article will explore the simplification of the algebraic expression (3n+4)^2 - (3n+2)^2. We will utilize the difference of squares pattern to efficiently achieve this.
Understanding the Difference of Squares Pattern
The difference of squares pattern is a fundamental algebraic concept that states: (a + b)(a - b) = a² - b²
This pattern allows us to factor a difference of two squares into the product of their sum and difference.
Applying the Pattern to Our Expression
Let's identify our 'a' and 'b' in our expression:
- a = 3n + 4
- b = 3n + 2
Now, applying the difference of squares pattern, we get:
(3n+4)² - (3n+2)² = (3n+4 + 3n+2)(3n+4 - 3n-2)
Simplifying the Result
We can now simplify the expression by combining like terms:
- (6n + 6)(2)
Further simplification leads to:
- 12n + 12
Conclusion
Therefore, the simplified form of the expression (3n+4)² - (3n+2)² is 12n + 12. By applying the difference of squares pattern, we were able to efficiently factor and simplify the original expression. This demonstrates the power of recognizing and utilizing algebraic patterns to streamline problem-solving.