Question
Question Uf \( C=r-8 \) and \( D=-r^{2}+8 r+7 \), find an expression that equals \( 2 C+2 D \) in standard form
Ask by French Ball. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2C + 2D = -2r^2 + 18r - 2 \)
Solution
To find an expression for \( 2C + 2D \) in standard form, follow these steps:
Given:
\[
C = r - 8
\]
\[
D = -r^2 + 8r + 7
\]
Calculate \( 2C + 2D \):
\[
2C + 2D = 2(r - 8) + 2(-r^2 + 8r + 7)
\]
Distribute the 2:
\[
= 2r - 16 + (-2r^2 + 16r + 14)
\]
Combine like terms:
\[
= -2r^2 + (2r + 16r) + (-16 + 14)
\]
\[
= -2r^2 + 18r - 2
\]
So, the expression in standard form is:
\[
-2r^2 + 18r - 2
\]
**Answer:**
After simplifying, an equivalent expression is –2 r² + 18 r – 2
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find \( 2C + 2D \), we first need to express \( C \) and \( D \) based on their definitions. Given: \( C = r - 8 \) \( D = -r^2 + 8r + 7 \) Now, calculate \( 2C \) and \( 2D \): \[ 2C = 2(r - 8) = 2r - 16 \] \[ 2D = 2(-r^2 + 8r + 7) = -2r^2 + 16r + 14 \] Next, add \( 2C \) and \( 2D \): \[ 2C + 2D = (2r - 16) + (-2r^2 + 16r + 14) \] Combine like terms: \[ 2C + 2D = -2r^2 + (2r + 16r) + (-16 + 14) \] \[ = -2r^2 + 18r - 2 \] Thus, the expression that equals \( 2C + 2D \) in standard form is: \[ \boxed{-2r^2 + 18r - 2} \]
