# ACT Math : How to use FOIL with the distributive property

## Example Questions

### Example Question #11 : Foil

FOIL:

Explanation:

By FOIL (First Outer Inner Last), we obtain –8x– 8x – 6x – 6.

Simplify: –8x2 – 14x – 6

### Example Question #11 : How To Use Foil With The Distributive Property

What is the product of the two real solutions of x+ 5x = 6?

1

1

6

6

6

Explanation:

x+ 5x – 6 = 0 factors to (x+6)(x1) = 0.

Therefore, the two real solutions are x = 6 and x = 1. Their product is simply 6.

### Example Question #13 : Foil

What is the value of (5 + 3i)(6 – 2i)?

20 – 8i

16 – 2i

12 + 8i

36 + 8i

24 + 8i

36 + 8i

Explanation:

We FOIL the equation to obtain 30 – 10i + 18i – 6i2, combining like terms and substituting i= –1,  we obtain 36 + 8i.

### Example Question #14 : Foil

Expand the following expression:

Explanation:

FOIL  and we get:

Then multiply it by  and get:

### Example Question #12 : Distributive Property

Expand using FOIL:

Explanation:

Step One: Expand

Step 2: Use the FOIL method

First:

Outside:

Inside:

Last:

Sum the products:

### Example Question #16 : Foil

Use the FOIL method to find the product. The answer must be in standard form.

Explanation:

Use the FOIL method to find the product.  The answer must be in standard form.

Step 1: Use the FOIL method

First:

Outside:

Inside:

Last:

Add these to find the product:

Step 2: Write the product in standard form

Standard form means the terms are written from highest degree to lowest degree. You find the degree of a term by adding the exponents in the term.

Therefore:

### Example Question #17 : Foil

Simplify:

Explanation:

Simplify:

Expand the equation and use the FOIL method:

First:

Outside:

Inside:

Last:

Sum the terms:

### Example Question #18 : Foil

Use FOIL to expand out the following product:

Explanation:

FOIL stands for First, Inside, Outside, Last. So multiply the first terms together:

The outside terms:

The inside terms:

and the last terms:

Now combine like terms:

### Example Question #13 : How To Use Foil With The Distributive Property

When is written in its form, where , , and  are integers, what is ?

Explanation:

In order to get the form, we must FOIL out .

FOIL is technique for distributing two binomials. The letters stand for First, Outer, Inner, and Last.

"First" stands for multiply the terms which occur first in each binomial.

"Outer" stands for multiply the outermost terms in the product.

"Inner" stands for multiply the innermost two terms.

"Last" stands for multiply the terms which occur last in each binomial.

Then, we must simplify the like terms, as shown below:

.

Here, , , while , so .

### Example Question #19 : Foil

What is the product of:

Explanation:

Use FOIL to multiply the products.
First terms:

Outside terms:

Inside terms:

Last terms:
Now combine like terms: