The expression you provided is:

\[ 2ax - 6ay + bx - 3by \]

This expression can be simplified or factored. Let's explore both options:

### 1. **Factor by grouping:**

We can group the terms to make factoring easier:

\[ (2ax - 6ay) + (bx - 3by) \]

Next, factor out the common factors from each group:

- From the first group \((2ax - 6ay)\), factor out \(2a\):

\[ 2a(x - 3y) \]

- From the second group \((bx - 3by)\), factor out \(b\):

\[ b(x - 3y) \]

Now, the expression becomes:

\[ 2a(x - 3y) + b(x - 3y) \]

Finally, factor out the common binomial factor \((x - 3y)\):

\[ (2a + b)(x - 3y) \]

So, the fully factored form of the expression is:

\[
(2a + b)(x - 3y)
\]

Would you like more details or have any questions?  

Here are 5 related questions for further practice:

1. How would you factor the expression \(3ax - 9ay + cx - 3cy\)?
2. Can you simplify the expression \(4ax + 2ay + bx + by\)?
3. How do you factor \(x^2y + 3xy^2 + 2x^2y + 6xy^2\)?
4. What is the factored form of \(6ax - 12ay + 2bx - 4by\)?
5. How do you simplify and factor \(ax + bx - ay - by\)?

**Tip:** When factoring by grouping, always look for common factors within each pair of terms to make the process easier.

Learn how to factorize the expression 2ax - 6ay + bx - 3by step-by-step with detailed explanations and examples. This problem covers algebraic factorization techniques, focusing on binomial factorization and grouping. Suitable for students in Grades 9-12.

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