To expand the expression \((2x + 3)(x - 5)\), you'll use the distributive property, also known as the FOIL method (First, Outer, Inner, Last) for binomials. Here's the step-by-step process:

1. **First:** Multiply the first terms in each binomial:  
   \[
   2x \cdot x = 2x^2
   \]

2. **Outer:** Multiply the outer terms:  
   \[
   2x \cdot (-5) = -10x
   \]

3. **Inner:** Multiply the inner terms:  
   \[
   3 \cdot x = 3x
   \]

4. **Last:** Multiply the last terms in each binomial:  
   \[
   3 \cdot (-5) = -15
   \]

5. **Combine all the terms:**  
   \[
   2x^2 - 10x + 3x - 15
   \]

6. **Simplify by combining like terms:**  
   \[
   2x^2 - 7x - 15
   \]

So, the expanded form of \((2x + 3)(x - 5)\) is \(\boxed{2x^2 - 7x - 15}\).

Would you like more details or have any questions?

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Here are some related questions to consider:

1. How do you factor the expression \(2x^2 - 7x - 15\)?
2. What is the process of expanding the expression \((2x + 3)(x + 5)\)?
3. How would the expansion change if the expression were \((2x + 3)(2x - 5)\)?
4. What happens if you expand a trinomial by a binomial?
5. Can you expand and simplify \((2x + 3)^2\)?
6. What is the significance of the distributive property in algebra?
7. How does the FOIL method apply to polynomials with more than two terms?
8. How do you determine the roots of the expanded polynomial \(2x^2 - 7x - 15\)?

**Tip:** Always double-check your expanded expressions to ensure all like terms are properly combined.

Learn how to expand the expression (2x + 3)(x - 5) using the FOIL method. This step-by-step solution covers algebraic concepts such as polynomials and the distributive property. Suitable for students in Grades 7-9.

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