Question
4. Show two different ways to factor \( -12 x+24-18 y \).
Ask by Warren Bowman. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There are two ways to factor the expression \( -12x + 24 - 18y \):
1. **Factoring out 6:**
\[
6(-2x + 4 - 3y)
\]
2. **Factoring out -6:**
\[
-6(2x - 4 + 3y)
\]
Both methods correctly factor the expression using different greatest common factors.
Solution
Certainly! Let's factor the expression \( -12x + 24 - 18y \) in two different ways by identifying different greatest common factors (GCF) and organizing the terms accordingly.
### **Method 1: Factoring Out 6**
1. **Identify the GCF:**
- The coefficients are -12, 24, and -18.
- The greatest common factor (GCF) of 12, 24, and 18 is **6**.
2. **Factor out 6:**
\[
-12x + 24 - 18y = 6(-2x + 4 - 3y)
\]
- **Explanation:**
- \(-12x ÷ 6 = -2x\)
- \(24 ÷ 6 = 4\)
- \(-18y ÷ 6 = -3y\)
3. **Final Factored Form:**
\[
6(-2x + 4 - 3y)
\]
### **Method 2: Factoring Out -6**
1. **Identify an Alternative GCF:**
- Sometimes, factoring out a negative GCF can simplify the expression or make certain properties clearer.
- Here, we choose **-6**.
2. **Factor out -6:**
\[
-12x + 24 - 18y = -6(2x - 4 + 3y)
\]
- **Explanation:**
- \(-12x ÷ -6 = 2x\)
- \(24 ÷ -6 = -4\)
- \(-18y ÷ -6 = 3y\)
3. **Final Factored Form:**
\[
-6(2x - 4 + 3y)
\]
### **Summary**
- **First Factoring:** \( 6(-2x + 4 - 3y) \)
- **Second Factoring:** \( -6(2x - 4 + 3y) \)
Both methods correctly factor the original expression but use different common factors, providing flexibility depending on the context or preferred form.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
First, let's rearrange the expression to group like terms: \( -12x - 18y + 24 \). We can factor by grouping. Notice we can factor out a common factor from the first two terms: \( -6(2x + 3y) + 24 \). Now, we can also factor out the 6 from \( 24 \): \( -6(2x + 3y) + 6 \times 4 \), which gives us \( 6(-2x - 3y + 4) \). Alternatively, we can factor by first finding the greatest common factor of all terms, which is 6. So, we factor out the 6 from the original equation: \( 6(-2x + 4 - 3y) \). From here, you can simplify inside the parentheses to show that you get the same expression in a neatly packed format!
