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The expression to simplify is \((3x - 6)(2x + 1)\), and the goal is to express this as a trinomial.

To expand this, we'll use the distributive property (also known as the FOIL method for binomials):

\[
(3x - 6)(2x + 1) = (3x)(2x) + (3x)(1) + (-6)(2x) + (-6)(1)
\]

Now, calculate each term:

\[
(3x)(2x) = 6x^2
\]
\[
(3x)(1) = 3x
\]
\[
(-6)(2x) = -12x
\]
\[
(-6)(1) = -6
\]

Now, combine like terms:

\[
6x^2 + 3x - 12x - 6 = 6x^2 - 9x - 6
\]

So the trinomial expression is:

\[
6x^2 - 9x - 6
\]

If you have any questions or want further details, feel free to ask!

### Related Questions:
1. How do you apply the distributive property to more complex polynomials?
2. What is the FOIL method, and how is it used in polynomial multiplication?
3. Can a trinomial always be factored back into two binomials?
4. How can this trinomial be factored?
5. What happens if one of the binomials has a coefficient of zero?

### Tip:
Always check if you can factor out any common terms from the final trinomial to simplify further!

Learn how to multiply binomials such as (3x - 6)(2x + 1) and express the result as a trinomial using the distributive property. A step-by-step guide for students in Grades 8-10, focusing on polynomial expansion techniques.

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