Using the FOIL method is simple. FOIL stands for First, Outside, Inside, Last. This is to help us make sure we multiply every term correctly looking at the terms inside of each parentheses. We follow FOIL to find the multiplied terms, then combine and simplify.

First, stands for multiply each first term of the seperate polynomials. In this case, .

Inner means we multiply the two inner terms of the expression. Here it's .

Outer means multiplying the two outer terms of the expression. For this expression we have .

Last stands for multiplying the last terms of the polynomials. So here it's .

Finally we combine the like terms together to get

.

We distribute each term in each parentheses to the terms of the other parentheses.

We get:

Which Simplifies:

We will arrange these from highest to lowest power, and adding a sign in between terms based on the coefficient of each term:

So, the answer is

First, we need to establish the dimensions of the box. We have the width, . The length is 4 more than 2 times the width, so we have , and the height is 5 more than the width, so we have .

We need to find the area. The area of a rectangular prism is given as length times width times height. So, we can write

To set it up using FOIL, it can be arranged as .

Through FOIL, we get , or .

First:

Outside:

Inside:

Last:

Add together:

First, factor out an , since it is present in all terms.

We need two factors that multiply to and add to .

and

Our factors are and .

We can check our answer using FOIL to get back to the original expression.

First:

Outside:

Inside:

Last:

Add together and combine like terms.

Distribute the that was factored out first.

Use the FOIL method to solve. Multiply the first term of the first binomial with both terms of the second binomial.

Multiply the second term of the first binomial with both terms of the second binomial.

Add the quantities by combining like-terms.

The answer is:

Even though the expression uses letters in the place where it is common to find numbers, we should recognize it is still the multiplication of two binomials, and the FOIL process can be used here.

F:

O:

I:

L:

So we have

Start by FOILing.

First:

Outer:

Inner:

Last:

Combine the terms:

Finally, simplify by combining like terms.

Even though there is an in one of the expressions, the expression is STILL a binomial, and should be treated as such. FOIL is used with the multiplication of two binomials, so FOIL works here.

F:

O:

I:

L:

Add the terms:

So FOIL works in this case

F:

O:

I:

L: