This problem involves multiplying two binomials. To solve, we will need to use the FOIL method.

Comparing this with our original equation, , , , and .

Using these values, we can substitute for the FOIL equation.

Notice that the two center terms use the same variables; this allows us to combine like terms.

To solve, it may be easier to convert the radicals to exponents.

Remember, the method used in multiplying two binomials is given by the equation:

Comparing this with our expression, we can identify the following variables:

We can substitute these values into the FOIL expression. Multiply to simplify.

Simplify by combining like terms. The center terms are equal and opposite, allowing them to cancel to zero.

A term to a given power can be combined with another term with the same base using the identity . This allows us to adjust our final answer.

Using the FOIL distribution method:

First: 

Outer: 

Inner: 

Last: 

Resulting in: 

Combining like terms, the 's cancel for a final answer of:

Using the FOIL distribution method:

First: 

Outer: 

Inner: 

Last: 

Resulting in: 

Combining like terms, the 's combine for a final answer of:

 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.

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 :