Question
If \( C=3 x-4 \) and \( B=-x^{2}-9 x-9 \), find an expression that equals \( 2 C+2 B \) in standard form.
Ask by Griffiths Wells. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2C + 2B = -2x^2 - 12x - 26 \)
Solution
To find an expression that equals \( 2C + 2B \) in standard form, follow these steps:
1. **Given:**
\[
C = 3x - 4 \quad \text{and} \quad B = -x^2 - 9x - 9
\]
2. **Calculate \( 2C \):**
\[
2C = 2(3x - 4) = 6x - 8
\]
3. **Calculate \( 2B \):**
\[
2B = 2(-x^2 - 9x - 9) = -2x^2 - 18x - 18
\]
4. **Add \( 2C \) and \( 2B \):**
\[
2C + 2B = (6x - 8) + (-2x^2 - 18x - 18)
\]
\[
= -2x^2 + (6x - 18x) + (-8 - 18)
\]
\[
= -2x^2 - 12x - 26
\]
5. **Final Expression in Standard Form:**
\[
2C + 2B = -2x^2 - 12x - 26
\]
**Answer:**
After simplifying, an equivalent standard form is –2 x² – 12 x – 26
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Simplify this solution Bonus Knowledge
To find \( 2C + 2B \), we start by calculating \( 2C \) and \( 2B \). 1. Calculate \( 2C \): \[ C = 3x - 4 \] \[ 2C = 2(3x - 4) = 6x - 8 \] 2. Calculate \( 2B \): \[ B = -x^2 - 9x - 9 \] \[ 2B = 2(-x^2 - 9x - 9) = -2x^2 - 18x - 18 \] 3. Now, we add \( 2C \) and \( 2B \): \[ 2C + 2B = (6x - 8) + (-2x^2 - 18x - 18) \] Combine like terms: \[ = -2x^2 + (6x - 18x) + (-8 - 18) \] \[ = -2x^2 - 12x - 26 \] Thus, the expression that equals \( 2C + 2B \) in standard form is: \[ \boxed{-2x^2 - 12x - 26} \]
