Factor by grouping.
xy plus 7 x plus 9 y plus 63

To factor the expression \(xy + 7x + 9y + 63\) by grouping, follow these steps:

1. **Group the terms**: Split the expression into two pairs of terms:
   \[
   (xy + 7x) + (9y + 63)
   \]

2. **Factor out the greatest common factor (GCF)** from each group:
   - In the first group \((xy + 7x)\), the GCF is \(x\):
     \[
     x(y + 7)
     \]
   - In the second group \((9y + 63)\), the GCF is \(9\):
     \[
     9(y + 7)
     \]

3. **Factor out the common binomial factor**:
   - Both groups now have the common binomial factor \((y + 7)\):
     \[
     x(y + 7) + 9(y + 7)
     \]

4. **Combine the factors**:
   - Factor out the common binomial \((y + 7)\):
     \[
     (x + 9)(y + 7)
     \]

So, the factored form of the expression \(xy + 7x + 9y + 63\) is:
\[
(x + 9)(y + 7)
\]

Would you like details on this process, or do you have any questions?

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Here are five related questions you might find interesting:
1. How would you factor the expression \(3xy + 6x + 2y + 4\) by grouping?
2. What is the factored form of \(2x^2y + 4xy + 3x + 6\)?
3. How can you verify that the factors \((x + 9)(y + 7)\) are correct?
4. What happens if you try to factor by grouping in an expression that isn't easily factorable?
5. How do you factor trinomials using a method similar to grouping?

**Tip:** When factoring by grouping, always check if there's a common factor across all terms before starting the grouping process.

Learn how to factor expressions by grouping with our step-by-step guide and examples. Explore the process of factoring the expression xy + 7x + 9y + 63 into its simplest form. Suitable for Grades 7-9.

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