To factor the expression \( 4 - 2x - 6y + 3xy \) by grouping, follow these steps:

1. **Group the terms** into two pairs:
   \[
   (4 - 2x) - (6y - 3xy)
   \]

2. **Factor out the common factors** from each group:
   - From the first group \( 4 - 2x \), factor out 2:
     \[
     2(2 - x)
     \]
   - From the second group \( -6y + 3xy \), factor out \( -3y \):
     \[
     -3y(2 - x)
     \]

3. Now, the expression looks like this:
   \[
   2(2 - x) - 3y(2 - x)
   \]

4. **Factor out the common binomial factor** \( (2 - x) \):
   \[
   (2 - x)(2 - 3y)
   \]

Thus, the expression \( 4 - 2x - 6y + 3xy \) factors to \( (2 - x)(2 - 3y) \).

Would you like more details or have any questions?

Here are 8 related questions you might find helpful:
1. How do you factor expressions that involve more than two terms?
2. Can you factor by grouping when there are no common factors in the pairs?
3. How do you factor a quadratic expression by grouping?
4. What is the difference between factoring by grouping and factoring completely?
5. Can you apply the grouping method to factor polynomials with four terms?
6. How do you handle grouping when the polynomial has negative signs?
7. What is the next step after factoring by grouping?
8. How do you know when an expression cannot be factored by grouping?

**Tip:** Always check for a common factor in each group when factoring by grouping.

Learn how to factor the expression 4 - 2x - 6y + 3xy using the grouping method. This detailed step-by-step solution covers algebraic concepts such as factoring and binomial factorization. Suitable for Grades 7-9.

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