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

1 Answer
Jul 29, 2015

Answer:

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.