xy + 3x + 6y + 18 Common Monomial Factor 

To factor the expression \( xy + 3x + 6y + 18 \) using the common monomial factor, follow these steps:

1. **Group the terms**: 
   \[
   (xy + 3x) + (6y + 18)
   \]

2. **Factor out the common factors from each group**:
   - From the first group \( xy + 3x \), the common factor is \( x \), so:
     \[
     x(y + 3)
     \]
   - From the second group \( 6y + 18 \), the common factor is \( 6 \), so:
     \[
     6(y + 3)
     \]

3. **Factor out the common binomial** \( (y + 3) \) from both terms:
   \[
   (y + 3)(x + 6)
   \]

So, the expression \( xy + 3x + 6y + 18 \) factors as:
\[
(y + 3)(x + 6)
\]

Would you like more details or have any questions?

Here are 8 related questions for practice:
1. Factor the expression \( ab + 2a + 3b + 6 \).
2. Find the common monomial factor in \( 2xy + 4x + 6y + 12 \).
3. Factor \( mn + 2m + 3n + 6 \) by grouping.
4. What is the common factor of \( 5x^2y + 10xy + 15y + 30 \)?
5. Factor \( 4xy + 8x + 12y + 24 \) completely.
6. How do you factor \( pq + 2p + 3q + 6 \)?
7. What is the result of factoring \( 7xy + 14x + 21y + 42 \)?
8. Factor \( a^2b + 3ab + 6a + 18 \) by grouping.

**Tip:** When factoring by grouping, always look for a common factor within pairs of terms first, then factor out the common binomial factor.

Learn how to factor the expression xy + 3x + 6y + 18 using the common monomial factor method. This problem involves grouping terms, identifying common factors, and factoring out a common binomial. Suitable for students in Grades 7-9.

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