(2n%2B6).jpeg "(4n+1)(2n+6)")
Exploring the Expression (4n+1)(2n+6)
The expression (4n+1)(2n+6) represents a product of two linear expressions. Let's dive into its properties, simplification, and potential applications.
Understanding the Expression
- Linear expressions: Both (4n+1) and (2n+6) are linear expressions because their highest power of the variable 'n' is 1.
- Product: The expression signifies the product of these two linear expressions.
Expanding the Expression
We can expand the expression using the distributive property (FOIL method):
(4n+1)(2n+6) = (4n * 2n) + (4n * 6) + (1 * 2n) + (1 * 6) = 8n² + 24n + 2n + 6 = 8n² + 26n + 6
Simplifying the Expression
The expanded form can be further simplified by combining like terms. This leads to the simplified expression: 8n² + 26n + 6
Applications
This expression can be used in various contexts, including:
- Algebraic manipulations: The expression can be used in solving equations, simplifying complex expressions, and proving algebraic identities.
- Quadratic equations: The simplified expression is a quadratic equation, which can be used to model real-world situations involving parabolic curves, like the trajectory of a projectile.
- Polynomial functions: The expression can represent a polynomial function, which can be graphed and analyzed to understand its behavior.
Conclusion
The expression (4n+1)(2n+6) represents a product of two linear expressions that can be expanded and simplified into a quadratic expression. This expression has various applications in algebraic manipulations, quadratic equations, and polynomial functions. Understanding its properties and simplifications can be useful in solving mathematical problems and interpreting real-world scenarios.