Which expression is equivalent to 6n-27? This mathematical inquiry delves into the intricacies of algebraic operations and the simplification of expressions. By exploring the fundamental concepts of factoring, greatest common factor (GCF), and grouping, we will unravel the steps involved in transforming 6n-27 into an equivalent expression that retains its mathematical essence.
Through a systematic approach, we will uncover the underlying principles that govern the simplification process, empowering you to tackle similar expressions with confidence. Real-world applications and related mathematical concepts will further enrich our understanding, highlighting the practical significance and interconnectedness of algebraic operations.
Equivalent Expression to 6n-27
The expression 6n-27 can be simplified by factoring out the greatest common factor (GCF), which is 3. The GCF is the largest factor that divides evenly into both terms of the expression.
To factor out the GCF, we first divide each term by 3:
“`
n-27 = 3(2n-9)
“`
The expression 2n-9 is now in factored form, and it is equivalent to the original expression 6n-27.
Simplifying the Expression, Which expression is equivalent to 6n-27
To simplify the expression 6n-27, we can use the following steps:
- Factor out the GCF, which is 3.
- Simplify the expression inside the parentheses.
- Combine like terms.
The following table shows the steps involved in simplifying the expression:
| Original Expression | Factors Being Grouped | Simplified Expression |
|---|---|---|
| 6n-27 | 3(2n-9) | 3(2n-9) |
| 3(2n-9) | 3(2(n-4)+3(-4)) | 3(2(n-4)-12) |
| 3(2(n-4)-12) | 3(2n-8-12) | 3(2n-20) |
The final simplified expression is 3(2n-20).
Applications of the Simplified Expression
The simplified expression 6n-27 can be applied in a variety of real-world scenarios, including:
- Calculating the perimeter of a rectangle with a length of 2n and a width of 9-3n.
- Finding the area of a triangle with a base of 2n and a height of 9-3n.
- Solving equations that involve the expression 6n-27.
Simplifying expressions can make it easier to solve problems and make calculations. It can also help to improve the clarity and efficiency of mathematical equations.
Related Mathematical Concepts
The expression 6n-27 is related to several mathematical concepts, including:
- Factoring
- GCF
- Algebraic operations
Factoring is the process of breaking down an expression into smaller factors. The GCF is the largest factor that divides evenly into all of the terms in an expression. Algebraic operations are the operations that are used to solve equations and simplify expressions, such as addition, subtraction, multiplication, and division.
Understanding these concepts is essential for solving mathematical problems. Factoring can be used to simplify expressions and solve equations. The GCF can be used to find the common factors in two or more expressions. Algebraic operations can be used to solve equations and simplify expressions.
FAQ Section: Which Expression Is Equivalent To 6n-27
What is the GCF of 6n and 27?
3
How do you factor out the GCF from 6n-27?
3(2n-9)
What are the steps involved in simplifying 6n-27?
1. Factor out the GCF (3) 2. Group the terms (2n and -9) 3. Factor out the GCF from each group (2 and -3) 4. Combine the factors (3(2n-3))
