Quadratic Equations - GED Math

Simplify using FOIL method.

Remember that multiplying variables means adding their exponents.

F:

O:

I:

L:

Combine the terms. Note that we cannot simplify further, as the exponents do not match and cannot be combined.

The FOIL method yields the products below.

First:

Outside:

Inside:

Last:

Add these four terms, and combine like terms, to obtain the product of the binomials.

First, factor out an , since it is present in all terms.

We need two factors that multiply to and add to .

and

Our factors are and .

We can check our answer using FOIL to get back to the original expression.

First:

Outside:

Inside:

Last:

Add together and combine like terms.

Distribute the that was factored out first.

Using the FOIL method is simple. FOIL stands for First, Outside, Inside, Last. This is to help us make sure we multiply every term correctly looking at the terms inside of each parentheses. We follow FOIL to find the multiplied terms, then combine and simplify.

First, stands for multiply each first term of the seperate polynomials. In this case, .

Inner means we multiply the two inner terms of the expression. Here it's .

Outer means multiplying the two outer terms of the expression. For this expression we have .

Last stands for multiplying the last terms of the polynomials. So here it's .

Finally we combine the like terms together to get

.

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:

First:

Outside:

Inside:

Last:

Add together:

FOIL:

First:

Outer:

Inner:

Last:

Add these together and combine like terms:

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 :

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: