231,446 views
44 votes
44 votes
Express as a trinomial. (x+1)(2x-8)
(x+1)(2x−8)

User Haeri
by
1.7k points

1 Answer

17 votes
17 votes

Answer: 2x^2-6x-8

====================================================

Step-by-step explanation:

Let y = x+1

This means (x+1)(2x-8) is the same as y(2x-8)

Distribute the y term through to get:

y(2x-8) = 2xy - 8y

Then plug y = x+1 back in and distribute twice more like so

2xy - 8y

2x( y ) - 8( y )

2x(x+1) - 8(x+1)

2x^2+2x - 8x-8

2x^2-6x-8

Therefore, (x+1)(2x-8) = 2x^2-6x-8

It is a trinomial because the result has three terms.

It's also a quadratic because the largest exponent is 2.

-------------------------------

Another approach is to use the FOIL rule

F: first

O: outer

I: inner

L: last

The first terms of (x+1) and (2x-8) are x and 2x respectively, so x*2x = 2x^2 is the product of them.

The outer terms are x and -8, which multiply to -8x

The inner terms are 1 and 2x which multiply to 2x

The last pair of terms are 1 and -8 which multiply to -8

We then get 2x^2-8x+2x-8 which turns into 2x^2-6x-8

-------------------------------

Another approach:

Perhaps my favorite approach is to use the box method. This is a grid like visual method to keep track of all the terms. See below.

We list the terms of x+1 along the left, and the terms of 2x-8 along the top. To fill out the inner boxes, we multiply the outside terms

For instance, x times 2x gets us 2x^2 in the upper left corner.

We have four boxes, so we'll have four products. Those terms being the terms from 2x^2-8x+2x-8 mentioned in the previous section. That combines to 2x^2-6x-8

Express as a trinomial. (x+1)(2x-8) (x+1)(2x−8)-example-1
User Michael Gendin
by
2.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.