To factor the expression xy + 4x + 2y + 8, we first look for common patterns and grouping possibilities within the terms.
1. **Grouping the Terms**: We can group the expression as follows:
- (xy + 2y) + (4x + 8)
2. **Factoring Out Common Factors**:
- In the first group (xy + 2y), we can factor out y:
y(x + 2) - In the second group (4x + 8), we can factor out 4:
4(x + 2)
3. **Putting It Together**: Now we rewrite the expression using our factored groups:
- y(x + 2) + 4(x + 2)
4. **Final Common Factor**: Notice that both terms contain the common factor (x + 2), so we can factor it out:
- (x + 2)(y + 4)
Thus, the factored form of the expression xy + 4x + 2y + 8 is:
- (x + 2)(y + 4)
This shows us that the original expression can be rewritten in this simpler form, making it easier to understand and work with.