If C, Equals, 2, M, Squared, Plus, MC=2m 2 +m And D, Equals, 2, Minus, 6, M, Plus, 2, M, Squared, CommaD=2−6m+2m 2 , Find An Expression That Equals 2, C, Minus, 2, D2C−2D In Standard Form
Introduction
In this article, we will explore the process of simplifying the expression 2C - 2D, where C = 2m^2 + m and D = 2 - 6m + 2m^2. We will use algebraic manipulation to rewrite the expression in standard form.
Understanding the Given Equations
Before we proceed, let's take a closer look at the given equations for C and D.
- C = 2m^2 + m
- D = 2 - 6m + 2m^2
Step 1: Substitute the Values of C and D into the Expression
To simplify the expression 2C - 2D, we need to substitute the values of C and D into the expression.
2C - 2D = 2(2m^2 + m) - 2(2 - 6m + 2m^2)
Step 2: Distribute the 2 to the Terms Inside the Parentheses
Now, let's distribute the 2 to the terms inside the parentheses.
2(2m^2 + m) = 4m^2 + 2m 2(2 - 6m + 2m^2) = 4 - 12m + 4m^2
Step 3: Rewrite the Expression with the Distributed Terms
Now, let's rewrite the expression with the distributed terms.
2C - 2D = (4m^2 + 2m) - (4 - 12m + 4m^2)
Step 4: Combine Like Terms
To simplify the expression further, let's combine like terms.
2C - 2D = 4m^2 + 2m - 4 + 12m - 4m^2
Step 5: Simplify the Expression
Now, let's simplify the expression by combining like terms.
2C - 2D = 4m^2 - 4m^2 + 2m + 12m - 4 2C - 2D = 14m - 4
Conclusion
In this article, we simplified the expression 2C - 2D, where C = 2m^2 + m and D = 2 - 6m + 2m^2. We used algebraic manipulation to rewrite the expression in standard form. The final expression is 14m - 4.
Key Takeaways
- To simplify the expression 2C - 2D, we need to substitute the values of C and D into the expression.
- We can distribute the 2 to the terms inside the parentheses to simplify the expression.
- Combining like terms is an essential step in simplifying the expression.
- The final expression is 14m - 4.
Final Answer
Q: What is the expression 2C - 2D, and how is it related to the given equations for C and D?
A: The expression 2C - 2D is a mathematical expression that involves the variables C and D. The given equations for C and D are C = 2m^2 + m and D = 2 - 6m + 2m^2. We need to substitute the values of C and D into the expression and simplify it.
Q: How do I substitute the values of C and D into the expression 2C - 2D?
A: To substitute the values of C and D into the expression 2C - 2D, we need to replace C with 2m^2 + m and D with 2 - 6m + 2m^2. This will give us the expression 2(2m^2 + m) - 2(2 - 6m + 2m^2).
Q: What is the next step after substituting the values of C and D into the expression?
A: After substituting the values of C and D into the expression, we need to distribute the 2 to the terms inside the parentheses. This will give us the expression 4m^2 + 2m - 4 + 12m - 4m^2.
Q: How do I simplify the expression 4m^2 + 2m - 4 + 12m - 4m^2?
A: To simplify the expression 4m^2 + 2m - 4 + 12m - 4m^2, we need to combine like terms. This will give us the expression 14m - 4.
Q: What is the final expression after simplifying 2C - 2D?
A: The final expression after simplifying 2C - 2D is 14m - 4.
Q: What are the key steps to simplify the expression 2C - 2D?
A: The key steps to simplify the expression 2C - 2D are:
- Substitute the values of C and D into the expression.
- Distribute the 2 to the terms inside the parentheses.
- Combine like terms to simplify the expression.
Q: What is the importance of simplifying mathematical expressions?
A: Simplifying mathematical expressions is important because it helps us to:
- Understand the underlying structure of the expression.
- Identify patterns and relationships between variables.
- Make calculations easier and more efficient.
- Solve problems more effectively.
Q: Can I use the same steps to simplify other mathematical expressions?
A: Yes, you can use the same steps to simplify other mathematical expressions. The key is to identify the variables and constants in the expression, substitute their values, distribute the coefficients, and combine like terms.
Conclusion
In this article, we answered frequently asked questions about simplifying the expression 2C - 2D. We covered topics such as substituting values, distributing coefficients, combining like terms, and the importance of simplifying mathematical expressions. We also provided a step-by-step guide on how to simplify the expression 2C - 2D.