(3k-4).jpeg "(2k+1)(3k-4)")
Exploring the Expression (2k + 1)(3k - 4)
The expression (2k + 1)(3k - 4) is a simple algebraic expression that represents the product of two binomials. Let's break down its components and explore its properties.
Understanding the Components
- Binomials: The expression consists of two binomials: (2k + 1) and (3k - 4). A binomial is a polynomial with two terms.
- Variables: The variable 'k' represents an unknown value.
- Coefficients: The numbers 2, 1, 3, and -4 are the coefficients that multiply the variables or constants.
Expanding the Expression
To fully understand the expression, we can expand it using the distributive property (also known as FOIL):
First: 2k * 3k = 6k² Outer: 2k * -4 = -8k Inner: 1 * 3k = 3k Last: 1 * -4 = -4
Combining like terms, we get:
(2k + 1)(3k - 4) = 6k² - 8k + 3k - 4 = 6k² - 5k - 4
Properties of the Expanded Expression
- Quadratic Expression: The expanded expression, 6k² - 5k - 4, is a quadratic expression. This means it has a highest power of 2 for the variable 'k'.
- Standard Form: The expression is in standard form, where the terms are arranged in descending order of their exponents.
Applications
This type of expression can be used in various mathematical contexts, including:
- Solving equations: The expression could be part of an equation to be solved for the variable 'k'.
- Factoring: The expression could be factored into its original binomials.
- Graphing: The expression could be used to represent a quadratic function and create a parabola on a graph.
- Real-world problems: The expression could be used to model real-world situations involving quadratic relationships.
Summary
The expression (2k + 1)(3k - 4) is a simple algebraic expression that can be expanded and manipulated to reveal its underlying properties and applications. Understanding how to expand and work with this type of expression is essential for solving various mathematical problems and understanding real-world phenomena.