Question

How do you write the product as a trinomial `(3x + 2)(2x - 3)`?

Answer 1

Multiply each term in one expression times each term in the other, then simplify by combining like terms.

Explanation:

There are other possible descriptions. Here is one of them:

To write the product `(3x + 2)(2x - 3)` in another form, we need to multiply each terms in `3x+2` times each term in `2x-3`.
(In algebra, 'terms' are things that are added together.)

So we need to multiply `3x` times `2x` and times `-3` (don't forget the minus sign!)
he we will multiply `2` times `2x` and times `-3` (again with the minus sign)

So here's how we can write that:

`(3x + 2)(2x - 3) = 3x(2x)+3x(-3) +2(2x)+2(-3)`

`= 6x^2-9x+4x-6`

Now I see two terms involving `x`, so we'll combine them into a single term:

`= 6x^2-5x-6`

Notice, now that we're finished, that the answer turns out to be a trinomial.

The instructions included the word 'trinomial' to try to make it clear that they didn't want us to rewrite the product in some other way -- like by changing the order, or by not combining like terms or doing some other way of rewriting.