Pregunta
If \( B=k-5 k^{2}-1 \) and \( C=k-2 k^{2} \), find an expression that equals \( 2 B+3 C \) in standard form.
Ask by Rodriquez Ford. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( 2B + 3C = -16k^{2} + 5k - 2 \)
Solución
To find the expression \( 2B + 3C \) in standard form, follow these steps:
1. **Given Equations:**
\[
B = k - 5k^{2} - 1
\]
\[
C = k - 2k^{2}
\]
2. **Calculate \( 2B \):**
\[
2B = 2(k - 5k^{2} - 1) = 2k - 10k^{2} - 2
\]
3. **Calculate \( 3C \):**
\[
3C = 3(k - 2k^{2}) = 3k - 6k^{2}
\]
4. **Add \( 2B \) and \( 3C \):**
\[
2B + 3C = (2k - 10k^{2} - 2) + (3k - 6k^{2}) = (2k + 3k) + (-10k^{2} - 6k^{2}) - 2
\]
\[
= 5k - 16k^{2} - 2
\]
5. **Write in Standard Form (descending order of powers):**
\[
-16k^{2} + 5k - 2
\]
**Final Answer:**
\[
2B + 3C = -16\,k^{2} + 5\,k - 2
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
To find the expression for \( 2B + 3C \), we first substitute the expressions for \( B \) and \( C \). Starting with: \[ B = k - 5k^2 - 1 \] \[ C = k - 2k^2 \] We calculate \( 2B \): \[ 2B = 2(k - 5k^2 - 1) = 2k - 10k^2 - 2 \] Next, we calculate \( 3C \): \[ 3C = 3(k - 2k^2) = 3k - 6k^2 \] Now we can combine \( 2B \) and \( 3C \): \[ 2B + 3C = (2k - 10k^2 - 2) + (3k - 6k^2) \] Combining like terms, we have: \[ = (2k + 3k) + (-10k^2 - 6k^2) - 2 \] \[ = 5k - 16k^2 - 2 \] Rearranging the expression in standard form gives us: \[ -16k^2 + 5k - 2 \] Thus, the expression equal to \( 2B + 3C \) in standard form is: \[ \boxed{-16k^2 + 5k - 2} \]
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