To expand \((-2x + 5y)(3x - 2y)\), follow the distributive property, often referred to as FOIL (First, Outer, Inner, Last) for binomials:

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

1. **First**: Multiply the first terms from each binomial:  
   \((-2x) \times (3x) = -6x^2\)

2. **Outer**: Multiply the outer terms:  
   \((-2x) \times (-2y) = 4xy\)

3. **Inner**: Multiply the inner terms:  
   \(5y \times (3x) = 15xy\)

4. **Last**: Multiply the last terms:  
   \(5y \times (-2y) = -10y^2\)

Now, combine the terms:

\[
-6x^2 + 4xy + 15xy - 10y^2
\]

Since \(4xy + 15xy = 19xy\), the expanded form is:

\[
-6x^2 + 19xy - 10y^2
\]

Would you like a more detailed explanation of the steps?

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Here are 5 related questions:
1. How do you expand \((x + 3)(x - 4)\)?
2. Can you explain how to factor \(x^2 - 7x + 10\)?
3. What is the result of expanding \((2a + b)(3a - 5b)\)?
4. How do you find the product of two trinomials?
5. What happens when you multiply \((x + y)(x + y)\)?

**Tip**: When expanding binomials, be sure to distribute each term from the first binomial to every term in the second.

Learn how to expand the binomial expression (-2x+5y)(3x-2y) using the FOIL method. This solution breaks down each step, including using the distributive property to multiply terms and combining like terms, resulting in the expanded form: -6x^2 + 19xy - 10y^2. Suitable for students in Grades 9-10.

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