(n-2).jpeg "(2n+3)(n-2)")
Expanding and Simplifying (2n+3)(n-2)
In mathematics, expressions like (2n+3)(n-2) are called binomials. To simplify such expressions, we need to use the distributive property of multiplication. This property states that multiplying a sum by a number is the same as multiplying each term of the sum by that number.
Expanding the Expression
To expand (2n+3)(n-2), we apply the distributive property twice:
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Distribute (2n+3) over (n-2): (2n+3)(n-2) = 2n(n-2) + 3(n-2)
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Distribute 2n and 3 over the terms inside the parentheses: 2n(n-2) + 3(n-2) = 2n² - 4n + 3n - 6
Simplifying the Expression
Now we combine the like terms:
2n² - 4n + 3n - 6 = 2n² - n - 6
The Final Result
Therefore, the expanded and simplified form of (2n+3)(n-2) is 2n² - n - 6.
Applications of Binomial Multiplication
The process of expanding and simplifying binomials is fundamental in algebra. It's used in various contexts like:
- Solving equations: The factored form (2n+3)(n-2) can be used to find the roots of the quadratic equation 2n² - n - 6 = 0.
- Graphing parabolas: The expanded form 2n² - n - 6 represents a parabola, allowing us to determine its shape and location on a graph.
- Factoring expressions: The factored form (2n+3)(n-2) can be used to find the factors of the expression 2n² - n - 6.
This simple example highlights the importance of understanding binomial multiplication in algebra. It forms the foundation for solving more complex problems and exploring various mathematical concepts.