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The expression \( 3a^{2}b - 4ab^{2} + 12ab \) factored is \( ab(3a - 4b + 12) \).
Solución
To factor the expression \( 3a^{2}b - 4ab^{2} + 12ab \), follow these steps:
1. **Identify the Greatest Common Factor (GCF):**
- **Terms:** \( 3a^{2}b \), \( -4ab^{2} \), and \( 12ab \).
- **Common factors:**
- **Numerical Coefficients:** The GCF of 3, -4, and 12 is 1 (since there's no common numerical factor other than 1).
- **Variables:** Each term contains at least \( a \) and \( b \).
So, the GCF is \( ab \).
2. **Factor Out the GCF:**
\[
3a^{2}b - 4ab^{2} + 12ab = ab(3a) - ab(4b) + ab(12)
\]
Simplify inside the parentheses:
\[
ab(3a - 4b + 12)
\]
3. **Final Factored Form:**
\[
3a^{2}b - 4ab^{2} + 12ab = ab(3a - 4b + 12)
\]
**Conclusion:**
The expression \( 3a^{2}b - 4ab^{2} + 12ab \) factored by its greatest common factor is:
\[
ab(3a - 4b + 12)
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Extra Insights
To factor the expression \( 3a^{2}b - 4ab^{2} + 12ab \), first, we'll look for common factors in each term. Here, \( ab \) is a common factor. Factor it out: \[ ab(3a - 4b + 12) \] Now, we can simplify the expression inside the parentheses if possible. However, \( 3a - 4b + 12 \) doesn’t easily factor further. So, the factored form of the expression is: \[ ab(3a - 4b + 12) \] If you were to evaluate this expression numerically, plugging in specific values for \( a \) and \( b \) can provide a solid understanding of how the quadratic behaves in real situations.
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