# Algebra 1 : How to use FOIL in the distributive property

## Example Questions

### Example Question #51 : Distributive Property

Multiply the following expression:

Explanation:

Start by using FOIL to multiply the two binomials:

Then, combine the middle terms of the trinomial in parentheses:

Finally, use the distributive property to multiply each term of the trinomial by :

Foil:

Explanation:

First:

Outside:

Inside:

Last:

### Example Question #51 : Distributive Property

FOIL .

Explanation:

(2x + 3)(x + 5)

First: 2x multiplied by x = 2x²

Outer: 2x multiplied by 5 = 10x

Inner: 3 multiplied by x = 3x

Lasts: 3 multiplied by 5 = 15

Put it all together: 2x² + 10x + 3x + 15

Simplify: 2x² + 13x + 15

### Example Question #1 : Equations

If the roots of a function are , what does the function look like in  format?

No equation of this form is possible.

Explanation:

This is a FOIL problem. First, we must set up the problem in a form we can use to create the function. To do this we take the opposite sign of each of the numbers and place them in this format: .

Now we can FOIL.

First:

Outside:

Inside:

Last:

Then add them together to get .

Combine like terms to find the answer, which is .

### Example Question #51 : Distributive Property

Expand:

Explanation:

Use the FOIL (First Outer Inner Last) method:

F:

O:

I:

L:

Put the terms together:

Simplify by combining like terms:

### Example Question #51 : How To Use Foil In The Distributive Property

Expand and then simplify:

Explanation:

Use the FOIL (First Outer Inner Last) method.

To start, focus on the first terms and multiply them together:

Next, multiply the last terms,  and , to get .

Finally, multiply the outside and inside terms, which should give you  and .

Combine the like terms:

This gives you the final answer, .

If instead your answer was , you simply forgot to subtract  at the end. If you got a different answer choice, you probably made a mistake with the signs when multiplying out the FOIL.

### Example Question #11 : Simplifying Polynomials

Simplify:

Explanation:

First, factor the numerator of the quotient term by recognizing the difference of squares:

Cancel out the common term from the numerator and denominator:

FOIL (First Outer Inner Last) the first two terms of the equation:

Combine like terms:

### Example Question #1 : Non Quadratic Polynomials

Create a cubic function that has roots at .

Explanation:

This can be written as:

Multiply the terms together:

Multiply the first two terms:

FOIL:

Combine like terms:

### Example Question #52 : How To Use Foil In The Distributive Property

Evaluate the following to its simplest form:

Explanation:

First we will foil the first function before distributing.

We will then distribute out the

We will then distribute out the

Now the only like terms we have are  and , so our final answer is:

### Example Question #51 : How To Use Foil In The Distributive Property

Simplify the expression: