Let's factor the expression \( 2xy - 5xy - 6px + 15py \).

### Step 1: Group the terms.
Group the terms in pairs to factor them more easily:

\[
(2xy - 5xy) - (6px - 15py)
\]

### Step 2: Factor out the common factors from each group.

1. **First group \( (2xy - 5xy) \):**
   \[
   2xy - 5xy = (2 - 5)xy = -3xy
   \]

2. **Second group \( -(6px - 15py) \):**
   \[
   -6px + 15py = -3p(2x - 5y)
   \]

Now the expression becomes:

\[
-3xy - 3p(2x - 5y)
\]

### Step 3: Factor out the common factor from the entire expression.

Notice that the common factor here is \(-3\), so we can factor that out:

\[
-3(xy + p(2x - 5y))
\]

This is the fully factored form of the expression.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you determine the greatest common factor (GCF) in an algebraic expression?
2. What are some strategies for grouping terms when factoring?
3. How can factoring by grouping be applied to more complex polynomials?
4. Why is it important to consider the sign when factoring expressions?
5. How does factoring help in solving algebraic equations?

**Tip:** When grouping terms for factoring, always look for common factors that can simplify the expression, and don't forget to check the signs of each term!

Learn how to factor the expression 2xy - 5xy - 6px + 15py step-by-step with detailed explanations. This problem covers algebraic concepts such as factoring polynomials and grouping terms. Suitable for Grades 7-9 students.

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