The question requires the problem to be solved with the FOIL method (First, Outer, Inner, Last). This describes the process by which you expand a binomial.

Four terms are created from the multiplication of two binomials before simplification.

For example:

So we can fill in our variables and simplify by combining like terms.

Use the FOIL method and combine like terms.

FOIL stands for:

First (multiply the first term in each binomial together)

Outer (multiply the outer terms of each binomial together)

Inner (multiply the inner terms of each binomial together)

Last (multiply the last term from each binomial together)

Using the FOIL method on the above binomials we get the following.

To combine these two binomials completely one must use the FOIL method. The FOIL method is just a way to distribute terms when there are 4 or more terms to be multiplied and it is based off the simpler distributive rule that one would use to combine say . The F stands for "multiply the first term in each parenthesis". The O stands for "multiply the outer terms in each parenthesis." The I represents the multiplication of the inner terms in each parenthesis. Finally the L stands for "mutliply the last term in each parenthesis." After these four steps are complete just combine like terms.

First lets multiply the first term (3x) by everything in the second set of parenthesis:

Can you see how this is the same as steps F (3x and 10) and O (3x and 4x)

Next we will multiply the inner term (2) by everything in the second set of parenthesis:

Can you see how this is equivalent to step I (2 and 10) and L (2 and 4x)?

Now combine like terms:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given , then:

First: 

Outer: 

Inner: 

Last: 

Thus, by FOIL:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given , then:

First: 

Outer: 

Inner: 

Last: 

Thus, by FOIL:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given , then:

First: 

Outer: 

Inner: 

Last: 

Thus, by FOIL:

Each value within one set of parentheses must be distributed to each value in the other set. To solve this problem, you can distribute :

Alternatively, you can distribute :

Then, grouping like factors together, you get the correct answer:

 is a special type of factorization.

When simplified, the "middle terms" cancel out, because they are the same value with opposite signs:

Expressions in the form  always simplify to  

At this point, we know that the only possible answers are q2 and -81.

However, now we have to check the terms of the second expression to see if we find any similarities.

Here we notice that rather than cancelling out, the middle terms combine instead of cancel. Also, our final term is the product of two negative numbers, and so is positive. Comparing the two simpified expressions, we find that only  is shared between them.

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given , then:

First: 

Outer: 

Inner: 

Last: 

Thus, by FOIL:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given , then:

First: 

Outer: 

Inner: 

Last: 

Thus, by FOIL: