Pregunta
If \( C=x^{2}-7 \) and \( D=2-x+9 x^{2} \), find an expression that equals \( C-2 D \) in standard form.
Ask by Love Barker. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( C - 2D = -17x^2 + 2x - 11 \)
Solución
To find the expression \( C - 2D \) where:
\[
C = x^2 - 7
\]
\[
D = 2 - x + 9x^2
\]
Follow these steps:
1. **Multiply \( D \) by 2:**
\[
2D = 2 \times (2) + 2 \times (-x) + 2 \times 9x^2 = 4 - 2x + 18x^2
\]
2. **Subtract \( 2D \) from \( C \):**
\[
C - 2D = (x^2 - 7) - (4 - 2x + 18x^2)
\]
3. **Distribute the negative sign:**
\[
C - 2D = x^2 - 7 - 4 + 2x - 18x^2
\]
4. **Combine like terms:**
\[
C - 2D = (x^2 - 18x^2) + 2x + (-7 - 4) = -17x^2 + 2x - 11
\]
**Final Answer:**
\[
-17x^2 + 2x - 11
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To find the expression that equals \( C - 2D \), we first need to substitute the given expressions for \( C \) and \( D \). Starting with: \[ C = x^{2} - 7 \] \[ D = 2 - x + 9x^{2} \] Now, we calculate \( 2D \): \[ 2D = 2(2 - x + 9x^{2}) = 4 - 2x + 18x^{2} \] Next, we can substitute \( C \) and \( 2D \) into the expression \( C - 2D \): \[ C - 2D = (x^{2} - 7) - (4 - 2x + 18x^{2}) \] Now, distribute the negative sign: \[ C - 2D = x^{2} - 7 - 4 + 2x - 18x^{2} \] Combining like terms, we have: \[ C - 2D = (x^{2} - 18x^{2}) + 2x + (-7 - 4) = -17x^{2} + 2x - 11 \] Thus, the expression that equals \( C - 2D \) in standard form is: \[ -17x^{2} + 2x - 11 \]
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