Quadratic Equations - GED Math
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Foil the two equations: 
and 
Foil the two equations:
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To foil these two equations, we'll need to multiply them together. To multiply them together, you'll have to take each term from the first equation and multiply them individually with each term in the second equation.
We'll start with 
from the first equation.
Multiply 
from the first equation with 
from the second equation.
Multiply 
from the first equation with 
from the second equation.
Now we'll use the 
from the first equation.
Multiply the 
from the first equation with the 
from the second equation.
Multiply the 
from the first equation with 
from the second equation.
We won't do this method with the second equation as that will only give us the same answer. Now take all of your answers and string them together, like so:
We can combine our 
and 
because they are under the same power of 
; which is one.
Since we cannot combine anymore like terms, we can take what we have left and put it as our final equation.
Your answer is 
To foil these two equations, we'll need to multiply them together. To multiply them together, you'll have to take each term from the first equation and multiply them individually with each term in the second equation.
We'll start with
Multiply
Multiply
Now we'll use the
Multiply the
Multiply the
We won't do this method with the second equation as that will only give us the same answer. Now take all of your answers and string them together, like so:
We can combine our
Since we cannot combine anymore like terms, we can take what we have left and put it as our final equation.
Your answer is
Simplify the following expression:
Simplify the following expression:
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Start by factoring the numerator.
To factor the numerator, you will need to find 
numbers that add up to 
and multiply to 
.
Next, factor the denominator.
To factor the denominator, you will need to find two numbers that add up to 
and multiply to 
.
Rewrite the fraction in its factored form.
Since 
is found in both numerator and denominator, they will cancel out.
Start by factoring the numerator.
To factor the numerator, you will need to find
Next, factor the denominator.
To factor the denominator, you will need to find two numbers that add up to
Rewrite the fraction in its factored form.
Since
Expand and combine like terms.
Expand and combine like terms.
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Using the FOIL distribution method:
First: 
Outer: 
Inner: 
Last: 
Resulting in: 
Combining like terms, the 
's combine for a final answer of:
Using the FOIL distribution method:
First:
Outer:
Inner:
Last:
Resulting in:
Combining like terms, the
What is the equation that has the following solutions? 
What is the equation that has the following solutions?
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This is a FOIL-ing problem. First, set up the numbers in a form we can use to create the function.
Take the opposite sign of each of the numbers and place them in this format. 
Multiply the 
in the first parentheses by the 
and 8 in the second parentheses respectively to get 
Multiply the 
in the first parentheses by the 
and 8 in the second parentheses as well to give us 
.
Then add them together to get 
Combine like terms to find the answer which is 
.
This is a FOIL-ing problem. First, set up the numbers in a form we can use to create the function.
Take the opposite sign of each of the numbers and place them in this format.
Multiply the
Multiply the
Then add them together to get
Combine like terms to find the answer which is
Simplify the following expression.
Simplify the following expression.
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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.
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.
Multiply the binomials below.
Multiply the binomials below.
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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.
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.
Factor the expression below.
Factor the expression below.
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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.
First, factor out an
We need two factors that multiply to
Our factors are
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
Simplify the following expression using the FOIL method:
Simplify the following expression using the FOIL method:
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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
.
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
FOIL the following expression.
FOIL the following expression.
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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.
This problem involves multiplying two binomials. To solve, we will need to use the FOIL method.
Comparing this with our original equation,
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.
FOIL the expression.
FOIL the expression.
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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.
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
Expand and combine like terms.
Expand and combine like terms.
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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
Multiply using the FOIL method:
Multiply using the FOIL method:
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First: 
Outside: 
Inside: 
Last: 
Add together:
First:
Outside:
Inside:
Last:
Add together:
Multiply:
Multiply:
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FOIL:
First: 
Outer:
Inner: 
Last: 
Add these together and combine like terms:
FOIL:
First:
Outer:
Inner:
Last:
Add these together and combine like terms:
Which terms do the following expressions share when simplified?
Which terms do the following expressions share when simplified?
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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.
When simplified, the "middle terms" cancel out, because they are the same value with opposite signs:
Expressions in the form
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
Use the distributive property (use FOIL method) to solve the following
Use the distributive property (use FOIL method) to solve the following
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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,
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,
Foil these two equations: 
and 
Foil these two equations:
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In order to foil these two equations, we're going to have to multiply them together. In order to do that, you're going to have to take each term from the first equation and separately multiply them with all the terms in the second equation.
First we'll start with 
from the first equation.
Multiply 
from the first equation with the 
from the second equation:
Multiply 
from the first equation with the 
from the second equation:
Now we'll work with the 
.
Multiply the 
from the first equation with the 
from the second equation:
Multiply the 
from the first equation with the 
from the second equation:
We won't do this again with the second equation as that will just give us the same answers. Now take all the answers and string them together into an equation like so:
The 
and 
can be combined together as they share the same power, which is one.
Since there is nothing left to combine, we can leave the equation as is.
Your answer should be 
In order to foil these two equations, we're going to have to multiply them together. In order to do that, you're going to have to take each term from the first equation and separately multiply them with all the terms in the second equation.
First we'll start with
Multiply
Multiply
Now we'll work with the
Multiply the
Multiply the
We won't do this again with the second equation as that will just give us the same answers. Now take all the answers and string them together into an equation like so:
The
Since there is nothing left to combine, we can leave the equation as is.
Your answer should be
Simplify the following using the distributive property of FOIL:
Simplify the following using the distributive property of FOIL:
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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
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
Simplify the following using the grid method for FOIL:
Simplify the following using the grid method for FOIL:
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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
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
Simplify:
Simplify:
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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).
First, multiply the first terms:
Next, multiply the last terms:
Now, multiply the inner and outer terms:
Combining all of these, you get:
Simplify:
Simplify:
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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 
:
All you need to do for this is to FOIL (or, distribute correctly). However, you must be careful because of the
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