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Simplificar. \[ \left(5 v^{2}-7 v-6\right)+\left(v^{2}-3 v+2\right) \]

Ask by Gibbs Bush. in Ecuador
Jan 13,2025

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Tutor-Verified Answer

Answer

La expresión simplificada es \(6v^{2} - 10v - 4\).

Solution

Para simplificar la expresión: \[ (5v^{2} - 7v - 6) + (v^{2} - 3v + 2) \] Suma los términos semejantes: 1. **Términos cuadráticos:** \[ 5v^{2} + v^{2} = 6v^{2} \] 2. **Términos lineales:** \[ -7v - 3v = -10v \] 3. **Términos constantes:** \[ -6 + 2 = -4 \] Al combinar todos los términos simplificados, obtenemos: \[ 6v^{2} - 10v - 4 \] **Respuesta final:** \[ 6v^{2} - 10v - 4 \]

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The Deep Dive

Para simplificar la expresión, primero sumamos los términos semejantes en el polinomio. Al juntar todos los términos, obtenemos: \[ (5v^{2} + v^{2}) + (-7v - 3v) + (-6 + 2) = 6v^{2} - 10v - 4 \] Así que la expresión simplificada es: \[ 6v^{2} - 10v - 4 \]

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