Question
Rewrite \( x^{4} y^{2}-3 x^{3} y^{3} \) using a common factor
Ask by Watson Todd. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The expression \( x^{4} y^{2} - 3 x^{3} y^{3} \) can be factored as \( x^{3} y^{2} (x - 3y) \).
Solution
To rewrite the expression \( x^{4} y^{2} - 3 x^{3} y^{3} \) using a common factor, follow these steps:
1. **Identify the Greatest Common Factor (GCF):**
- For the terms \( x^{4} y^{2} \) and \( -3 x^{3} y^{3} \), the GCF is \( x^{3} y^{2} \).
2. **Factor out the GCF:**
- Divide each term by the GCF:
\[
x^{4} y^{2} \div x^{3} y^{2} = x
\]
\[
-3 x^{3} y^{3} \div x^{3} y^{2} = -3y
\]
3. **Write the Factored Form:**
- Combine the GCF with the remaining terms:
\[
x^{3} y^{2} (x - 3y)
\]
**Final Answer:**
\[
x^{3} y^{2} (x - 3y)
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Extra Insights
You can factor the expression \( x^{4} y^{2}-3 x^{3} y^{3} \) by identifying the common factors in both terms. The common factor here is \( x^{3} y^{2} \). So, you can rewrite the expression as: \[ x^{3} y^{2} \left( x - 3y \right) \] Now you have a factored form that showcases the common factor beautifully!
