# GED Math : Quadratic Equations

## Example Questions

### Example Question #74 : How To Use Foil In The Distributive Property

Which terms do the following expressions share when simplified?

only

and

and

and

and

only

Explanation:

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.

### Example Question #4940 : Algebra 1

Use the distributive property (use FOIL method) to solve the following

Explanation:

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:

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

### Example Question #133 : Distributive Property

Simplify the following using the distributive property of FOIL:

Explanation:

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

### Example Question #11 : Foil

Simplify the following using the grid method for FOIL:

Explanation:

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

### Example Question #11 : Foil

Simplify:

Explanation:

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:

### Example Question #11 : Foil

Simplify:

Explanation:

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 :

### Example Question #13 : Foil

Simplify:

Explanation:

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:

### Example Question #14 : Foil

Solve:

Explanation:

Use the FOIL method to solve this expression.

Simplify each term.

Combine like-terms.

### Example Question #15 : Foil

Solve:

Explanation:

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.

Solve: