Question
Question If \( C=2 m^{2}+m \) and \( D=2-6 m+2 m^{2} \), find an expression that equals \( 2 C-2 D \) in standard form.
Ask by Ford Logan. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2C - 2D = 14m - 4 \)
Solution
To find an expression for \( 2C - 2D \) in standard form, follow these steps:
**Given:**
\[
C = 2m^{2} + m
\]
\[
D = 2 - 6m + 2m^{2}
\]
**Step 1: Calculate \( 2C \)**
\[
2C = 2 \times (2m^{2} + m) = 4m^{2} + 2m
\]
**Step 2: Calculate \( 2D \)**
\[
2D = 2 \times (2 - 6m + 2m^{2}) = 4 - 12m + 4m^{2}
\]
**Step 3: Subtract \( 2D \) from \( 2C \)**
\[
2C - 2D = (4m^{2} + 2m) - (4 - 12m + 4m^{2})
\]
**Step 4: Distribute the negative sign and combine like terms**
\[
2C - 2D = 4m^{2} + 2m - 4 + 12m - 4m^{2}
\]
\[
2C - 2D = (4m^{2} - 4m^{2}) + (2m + 12m) - 4
\]
\[
2C - 2D = 0m^{2} + 14m - 4
\]
\[
2C - 2D = 14m - 4
\]
**Final Answer:**
\[
2C - 2D = 14m - 4
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the expression that equals \( 2C - 2D \), we first need to compute \( 2C \) and \( 2D \). Starting with \( C \): \[ C = 2m^2 + m \] So, \[ 2C = 2(2m^2 + m) = 4m^2 + 2m \] Now for \( D \): \[ D = 2 - 6m + 2m^2 \] So, \[ 2D = 2(2 - 6m + 2m^2) = 4 - 12m + 4m^2 \] Now we can substitute these into our expression: \[ 2C - 2D = (4m^2 + 2m) - (4 - 12m + 4m^2) \] Distributing the negative sign: \[ 2C - 2D = 4m^2 + 2m - 4 + 12m - 4m^2 \] Combining like terms: \[ (4m^2 - 4m^2) + (2m + 12m) - 4 = 0 + 14m - 4 \] This simplifies to: \[ 2C - 2D = 14m - 4 \] To express this in standard form, we can write: \[ 2C - 2D = 14m - 4 \] Thus, the expression in standard form is \( 14m - 4 \).
