Pregunta
Factor by grouping: \[ r s+7 s^{2}-r-7 s \] SUBMIT ANSWER
Ask by Blake May. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The factored form is \( (r + 7s)(s - 1) \).
Solución
We start with the expression:
\[
rs + 7s^2 - r - 7s
\]
**Step 1: Group the terms.**
Group the expression into two sets:
\[
(rs + 7s^2) + (-r - 7s)
\]
**Step 2: Factor out the common factors from each group.**
From the first group \(rs + 7s^2\), factor out \(s\):
\[
s(r + 7s)
\]
From the second group \(-r - 7s\), factor out \(-1\):
\[
-1(r + 7s)
\]
**Step 3: Factor out the common binomial.**
Now the expression becomes:
\[
s(r + 7s) - 1(r + 7s)
\]
Factor out the common binomial \((r + 7s)\):
\[
(r + 7s)(s - 1)
\]
Thus, the factored form is:
\[
\boxed{(r + 7s)(s - 1)}
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Bonus Knowledge
To factor the expression \( r s + 7 s^{2} - r - 7 s \) by grouping, we can follow these steps: 1. Group the terms: \( (r s - r) + (7 s^{2} - 7 s) \). 2. Factor out the common factors in each group: - From the first group \( r s - r \), we can factor out \( r \), giving us \( r(s - 1) \). - From the second group \( 7 s^{2} - 7 s \), we can factor out \( 7 s \), giving us \( 7 s(s - 1) \). 3. Now our expression looks like this: \( r(s - 1) + 7 s(s - 1) \). 4. Notice that \( (s - 1) \) is a common factor: - So we can factor out \( (s - 1) \): \[ (s - 1)(r + 7 s). \] Thus, the factored form of the expression is: \[ (s - 1)(r + 7 s). \]
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
