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

Jul 29, 2015

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 $\left(3 x + 2\right) \left(2 x - 3\right)$ in another form, we need to multiply each terms in $3 x + 2$ times each term in $2 x - 3$.
(In algebra, 'terms' are things that are added together.)

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

So here's how we can write that:

$\left(3 x + 2\right) \left(2 x - 3\right) = 3 x \left(2 x\right) + 3 x \left(- 3\right) + 2 \left(2 x\right) + 2 \left(- 3\right)$

$= 6 {x}^{2} - 9 x + 4 x - 6$

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

$= 6 {x}^{2} - 5 x - 6$

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.