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The problem asks to express the given expression \((2x + 3)(3x - 5)\) as a trinomial. To do this, we will expand the expression using the distributive property, often called the FOIL method (First, Outer, Inner, Last).

Let's apply the steps to expand:

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

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

3. **Inner:** Multiply the inner terms:  
   \(3 \times 3x = 9x\)

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

Now, combine all these results:
\[6x^2 - 10x + 9x - 15\]

Combine the like terms:
\[6x^2 - x - 15\]

So, the trinomial form of the expression \((2x + 3)(3x - 5)\) is:
\[6x^2 - x - 15\]

Would you like more details or have any questions about this?

Here are some related questions:
1. What is the FOIL method, and when do you use it?
2. How do you combine like terms in polynomial expressions?
3. What is the difference between a binomial and a trinomial?
4. How can you check your answer when expanding polynomials?
5. What other methods can be used to expand binomials?

**Tip:** When expanding binomials, always check each multiplication step carefully to avoid sign errors!

Learn how to expand the binomials (2x + 3)(3x - 5) using the FOIL method and express the result as a trinomial. This algebra problem involves key concepts such as the distributive property and polynomial expansion, suitable for students in Grades 7-9.

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