# ACT Math : How to subtract trinomials

## Example Questions

### Example Question #11 : Trinomials

A hockey team has 12 forwards, 6 defensemen, and 2 goalies.  When they place 3 forwards, 2 defensemen, and 1 goalie on the ice, how many of each type are on the bench, (not on the ice)?  F=Forward, D = Defensemen, G= Goalie

15 F, 8 D, 3 G

9 F, 4 D, 1 G

6 F, 2 D, 1 G

36 F, 12 D, 2 G

4 F, 3 D, 2 G

9 F, 4 D, 1 G

Explanation:

We can represent this as a subtraction of trinomials.

(12F + 6D + 2G) – (3F + 2D + 1G) = 9F + 4D + 1G.

### Example Question #2 : How To Subtract Trinomials

You go to the grocery store and pick up  apples,  peaches, and  oranges. Today you had some friends over who ate  apples,  peaches, and  oranges. Which of the following represents how many of each you now have left if  = apples,  = peaches, and  = oranges?

Explanation:

1. Represent the situation with two sets of trinomials:

Before your friends ate the fruit:

2. Subtract the first trinomial from the second trinomial:

### Example Question #3 : How To Subtract Trinomials

Choose the answer which best simplifies the following expression:

Explanation:

To solve this expression, merely remove the parentheses (bearing in mind that because the second trinomial is being subtracted, it will be negative) and combine like terms:

### Example Question #4 : How To Subtract Trinomials

Choose the answer which best simplifies the following expression:

Explanation:

To simplify, remove parentheses and combine like terms:

### Example Question #5 : How To Subtract Trinomials

Choose the answer which best simplifies the following expression: