Question
\( C=2 y-1 \) and \( D=y-y^{2} \), find an expression that eqpals \( 3 C+D \) in standard
Ask by Knight Gonzalez. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 3C + D = -y^2 + 7y - 3 \)
Solution
To find an expression equivalent to \( 3C + D \) in standard form, follow these steps:
1. **Given Equations:**
\[
C = 2y - 1
\]
\[
D = y - y^2
\]
2. **Multiply \( C \) by 3:**
\[
3C = 3(2y - 1) = 6y - 3
\]
3. **Add \( D \) to \( 3C \):**
\[
3C + D = (6y - 3) + (y - y^2)
\]
4. **Combine Like Terms:**
\[
3C + D = 6y + y - y^2 - 3 = 7y - y^2 - 3
\]
5. **Arrange in Standard Polynomial Form (Descending Powers of \( y \)):**
\[
3C + D = -y^2 + 7y - 3
\]
**Final Answer:**
\[
3C + D = -y^2 + 7y - 3
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To find an expression that equals \( 3C + D \), we start by substituting the given equations: 1. \( C = 2y - 1 \) 2. \( D = y - y^2 \) Now, calculate \( 3C \): \[ 3C = 3(2y - 1) = 6y - 3 \] Next, we add \( D \) to this expression: \[ 3C + D = (6y - 3) + (y - y^2) \] Combining the like terms gives: \[ 3C + D = 6y - 3 + y - y^2 = (6y + y) - y^2 - 3 \] This simplifies to: \[ 3C + D = 7y - y^2 - 3 \] To express this in standard form, we rearrange it: \[ 3C + D = -y^2 + 7y - 3 \] Thus, the expression in standard form is: \[ 3C + D = -y^2 + 7y - 3 \]
