2. Factor by grouping. yw-28y-4w+7y?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Factor by grouping
![**Problem 2: Factor by Grouping**
Expression to factor:
\[ yw - 28y - 4w + 7y^2 \]
**Instructions for an Educational Website:**
To factor the expression by grouping, follow these steps:
1. **Group the terms:**
- Group the first two terms and the last two terms: \( (yw - 28y) \) and \( (-4w + 7y^2) \).
2. **Factor out the greatest common factor from each group:**
- For the first group \( (yw - 28y) \), factor out \( y \):
\[ y(w - 28) \]
- For the second group \( (-4w + 7y^2) \), factor out \( -1 \) (pay attention to signs):
\[ -1(4w - 7y^2) \]
3. **Rewrite the expression:**
- After factoring, the expression becomes:
\[ y(w - 28) - 1(4w - 7y^2) \]
4. **Factor by grouping:**
- The expression can further be analyzed, although additional steps may reveal alternative factors.
This method simplifies expressions by identifying common factors and grouping strategically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa78d0b28-f8d9-4005-972e-85b11c340109%2Fae2a7bf9-45ea-48b3-84f2-7d2f94d057c3%2F0feqoc3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 2: Factor by Grouping**
Expression to factor:
\[ yw - 28y - 4w + 7y^2 \]
**Instructions for an Educational Website:**
To factor the expression by grouping, follow these steps:
1. **Group the terms:**
- Group the first two terms and the last two terms: \( (yw - 28y) \) and \( (-4w + 7y^2) \).
2. **Factor out the greatest common factor from each group:**
- For the first group \( (yw - 28y) \), factor out \( y \):
\[ y(w - 28) \]
- For the second group \( (-4w + 7y^2) \), factor out \( -1 \) (pay attention to signs):
\[ -1(4w - 7y^2) \]
3. **Rewrite the expression:**
- After factoring, the expression becomes:
\[ y(w - 28) - 1(4w - 7y^2) \]
4. **Factor by grouping:**
- The expression can further be analyzed, although additional steps may reveal alternative factors.
This method simplifies expressions by identifying common factors and grouping strategically.
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