Remember that FOIL stands for First, Outer, Inner, Last. We will add up the different parts. If we had an expression

than we would have

First: 

Outer: 

Inner: 

Last: 

For this problem we have

First: 

Outer: 

Inner: 

Last: 

Adding these together gives

check: let's add the first two numbers and multiply that by the sum of the last two,

When using the FOIL method to distribute, we do the following:

FIRST

OUTSIDE

INSIDE

LAST

In other words, we multiply the first terms, the outside terms, the inside terms, and the last terms.

FIRST 

OUTSIDE 

INSIDE 

LAST 

Now, we combine all the terms.  We get

We can simplify, and we are left with

To solve using the grid method, we use the given problem

and create a grid using each term.

Now, we fill in the boxes by multiplying the terms in each row and column.

Now, we write each of the multiplied terms out,

We combine like terms.

Therefore, by using the grid method, we get the solution

All you need to do for this is to FOIL (or, distribute correctly).

First, multiply the first terms:

Next, multiply the last terms:

Now, multiply the inner and outer terms:

Combining all of these, you get:

All you need to do for this is to FOIL (or, distribute correctly).  However, you must be careful because of the  in front of the groups.  Just leave that for the end.  First, FOIL the groups.

4(x+3)(2x-2)

First, multiply the first terms:

Next, multiply the last terms:

Now, multiply the inner and outer terms:

Combining all of these, you get:

Then, multiply everything by :

You just need to methodically multiply for these kinds of questions.  However, first move around your groups to make your life a bit easier.  Look at the problem this way:

Now, the first pair is a difference of squares, so you can multiply that out quickly!

After this, you are in a FOIL case.

Start by multiplying the first terms:

Then, multiply the final terms:

Then, multiply the inner and outer terms:

Now, combine them all:

Use the FOIL method to solve this expression.

Simplify each term.

Combine like-terms.

The answer is:  

Apply the FOIL method to solve this problem.

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 both quantities.

The answer is:  

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:   

The greatest common factor of the three terms is , so factor it out, and distribute it out, as follows:

The trinomial  might be factored out as the product of two binomials , where  and  have sum 7 and product 12; by trial and error, we find that two such integers do exist, and they are 3 and 4. Therefore, 

,

the correct factorization.