Pregunta
Factor the polynomial by grouping: \( 6a^{2}b + 9ab^{2} - 4a - 6b \)
Ask by Lee Carroll. in South Africa
Jan 12,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The polynomial \( 6a^{2}b + 9ab^{2} - 4a - 6b \) factors to \( (2a + 3b)(3ab - 2) \).
Solución
To factor the polynomial \( 6a^{2}b + 9ab^{2} - 4a - 6b \) by grouping, follow these steps:
1. **Group the Terms:**
\[
(6a^{2}b + 9ab^{2}) + (-4a - 6b)
\]
2. **Factor Out the Greatest Common Factor (GCF) from Each Group:**
- From the first group \( 6a^{2}b + 9ab^{2} \), the GCF is \( 3ab \):
\[
3ab(2a + 3b)
\]
- From the second group \( -4a - 6b \), the GCF is \( -2 \):
\[
-2(2a + 3b)
\]
3. **Rewrite the Expression with the Factored Groups:**
\[
3ab(2a + 3b) - 2(2a + 3b)
\]
4. **Factor Out the Common Binomial Factor \( (2a + 3b) \):**
\[
(2a + 3b)(3ab - 2)
\]
**Final Factored Form:**
\[
(2a + 3b)(3ab - 2)
\]
Answer: \((2a + 3b)(3ab - 2)\)
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To factor the polynomial \( 6a^{2}b + 9ab^{2} - 4a - 6b \) by grouping, we can first rearrange and group the terms as follows: \[ (6a^{2}b + 9ab^{2}) + (-4a - 6b) \] Now we can factor each group: From the first group \( 6a^{2}b + 9ab^{2} \), we can factor out \( 3ab \): \[ 3ab(2a + 3b) \] From the second group \( -4a - 6b \), we can factor out \( -2 \): \[ -2(2a + 3b) \] Now, we can combine the two factored groups: \[ 3ab(2a + 3b) - 2(2a + 3b) \] We can now factor out the common factor \( (2a + 3b) \): \[ (2a + 3b)(3ab - 2) \] Thus, the factorization of the polynomial \( 6a^{2}b + 9ab^{2} - 4a - 6b \) by grouping is: \[ (2a + 3b)(3ab - 2) \]
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