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.

Expand the following expression:

Do you recall FOIL? It is an acronym to help us remember to multiply each pair of terms when multiplying binomials.

First: Multiply the pair of first terms in this case 6x and 9x

Outer: Multiply the terms furthest to the left and right. In this case 6x and 3

Inner: Multiply the middle two terms -4 and 9x

Last: The last term from each group, in this case -4 and 3

Now, we just need to put the terms together:

And we have:

Take the product of the two binomials  using the FOIL method.

First: 

Outer: 

Inner: 

Last: 

Add these:

Collect the like terms in the middle by subtracting coefficients:

Therefore, 

Distribute the  by multiplying it by each term:

,

the correct product.

Expand the following expression:

This is what is known as a difference of squares. We can use FOIL to find our answer.

Remember FOIL? First Outer Inner Last

This means we need to multiply each pair of terms in parentheses to get the correct answer:

First:

Outer:

Inner:

Last:

Put it all together to get:

Making our answer 

Do you see why it's called a difference of squares?

Start by FOILing.

First: 

Outer: 

Inner: 

Last: 

Combine the terms:

Finally, simplify by combining like terms.

You must FOIL the two terms.

Now, combine like terms.

Thus, the expanded version of the given terms is the following: