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Welcome to the F.O.I.L. method!
Let’s Get Started!
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The purpose of this program is to teach you the basics of multiplying two polynomials together
using the aid of the F.O.I.L. method.
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How to Navigate this Program
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The following arrow will be seen on most screens and when clicked on will take you to the next page. It will be located in the lower right-hand corner.
How to Navigate this Program
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How to Navigate this Program
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The question mark located in the top right screen will bring you to a page that reminds you exactly what all of the tooltips do for you.
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The button that looks like a home located in the middle of the bottom of the page brings you back to the most recent selection screen.
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F.O.I.L. FUN
What is the F.O.I.L Method?
Teach Me How to F.O.I.L
Let Me Practice
I’m Ready for the Quiz
So what exactly is the FOIL method?
The FOIL method is a simple way to make sure that you multiply
polynomials together in the correct way.
The FOIL method is only used for binomial polynomials, however.
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What exactly is a binomial polynomial and how does it concern me?
Chances are, you have probably encountered a binomial before.
A binomial is an expression that consists of two terms.Examples of these are:
x + 4, x2 – 1, x + 18, x + 5, –8 + 7x
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How does this tie into FOIL?
So, by now you are probably wondering what FOIL stands for and how it ties into multiplying together binomials. FOIL is an acronym for the
following:FirstOuterInnerLast
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So you want to learn how to FOIL?
To begin, let us look at two binomial expressions that we wish to multiply together. For
demonstration purposes we are going to look at the following two polynomials:
(x + 3) & (x + 4)And we are going to multiply them together
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The F of FOIL
To begin using FOIL, we multiply together the first part of each of the two binomials.
(x + 3) * (x + 4)x * x = x2
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The O of FOIL
The second step of FOIL is to multiply together the outer part of each binomial. Remember that the sign of each term in the expression matters.
(x + 3) * (x + 4)x * 4 = 4x
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We’re Halfway Done
We have gotten halfway through FOIL so make sure you understand why we currently have:
x2 + 4x
If you are unsure how we got this make sure you go back and review a little bit.
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The I of FOIL
The third step of FOIL is to multiply the inner terms of each binomial together.
(x + 3) * (x + 4)3 * x = 3x
Adding this to what we already have gives us x2 + 4x + 3x
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The L of FOIL
The final step of FOIL is to multiply the last terms of each of the binomials together.
(x + 3) * (x + 4)3 * 4 = 12
We finally have x2 + 3x + 4x +12But wait! There is more!
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The Secret Step
There is a secret step that is not talked about in the acronym FOIL! This step is an important one,
and it is to reduce like terms.x2 + 3x + 4x + 12
Since the x in these two terms are both to the same power, they can be combined together
making the final answer… DRUMROLL PLEASE
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Click next to see more problems worked out.
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x2 + 7x +12
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Practice
Practice Understanding FOIL
Practice Problems
Main Menu
So Let’s Make Sure We Know What FOIL Means
The F in FOIL stands for which of the following?
FamousFirst
FriendFreak
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You Guessed Wrong!
That is not what the F in FOIL stands for!
Review the FOIL method if you forget.
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That is Correct!
The F in FOIL stands for First!Good Job! Now click on the first terms.
(x + 3) * (x + 4)
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That is Correct!
Now Click the other First term
(x + 3) * (x + 4)
Home
SILLY
You already clicked on that!
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Good Job!
You know your F in FOILDoing good so far!
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That is Correct!
Now Click the other First term
(x + 3) * (x + 4)
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Incorrect
That is not one of the first terms.
Go back and Review
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That is Correct!
Now Click the other First term
(x + 3) * (x + 4)
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SILLY
You already clicked on that!
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Good Job!
You know your F in FOILDoing good so far!
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Incorrect
That is not one of the first terms.
Go back and Review
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Incorrect
That is not one of the first terms.
Go back and Review
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So Let’s Make Sure We Know What FOIL Means
The O in FOIL stands for which of the following?
OuterOmitOddOops
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You Guessed Wrong!
That is not what the O in FOIL stands for!
Review the FOIL method if you forget.
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That is Correct!
The O in FOIL stands for Outer!Good Job! Now click on the outer terms.
(x + 3) * (x + 4)
Home
That is Correct!
Now Click the other Outer term
(x + 3) * (x + 4)
Home
That is Correct!
Now Click the other Outer term
(x + 3) * (x + 4)
Home
Incorrect
That is not one of the outer terms.
Go back and Review
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Incorrect
That is not one of the outer terms.
Go back and Review
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Incorrect
That is not one of the outer terms.
Go back and Review
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SILLY
You already clicked on that!
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SILLY
You already clicked on that!
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Good Job!
You know your O in FOILDoing good so far!
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So Let’s Make Sure We Know What FOIL Means
The I in FOIL stands for which of the following?
IDKIndeedInner
Imagine
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You Guessed Wrong!
That is not what the I in FOIL stands for!
Review the FOIL method if you forget.
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That is Correct!
The I in FOIL stands for Inner!Good Job! Now click on the inner terms.
(x + 3) * (x + 4)
Home
That is Correct!
Now Click the other Inner term
(x + 3) * (x + 4)
Home
That is Correct!
Now Click the other Inner term
(x + 3) * (x + 4)
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Incorrect
That is not one of the Inner terms.
Go back and Review
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Incorrect
That is not one of the Inner terms.
Go back and Review
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Incorrect
That is not one of the Inner terms.
Go back and Review
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SILLY
You already clicked on that!
Last Home
SILLY
You already clicked on that!
Last Home
Good Job!
You know your I in FOILDoing good so far!
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So Let’s Make Sure We Know What FOIL Means
The L in FOIL stands for which of the following?
LameLeftLast
Lucky
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You Guessed Wrong!
That is not what the L in FOIL stands for!
Review the FOIL method if you forget.
Last Home
That is Correct!
The L in FOIL stands for Last!Good Job! Now click on the last terms.
(x + 3) * (x + 4)
Home
That is Correct!
Now Click the other Last term
(x + 3) * (x + 4)
Home
That is Correct!
Now Click the other Last term
(x + 3) * (x + 4)
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Incorrect
That is not one of the Last terms.
Go back and Review
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Incorrect
That is not one of the Last terms.
Go back and Review
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Incorrect
That is not one of the Last terms.
Go back and Review
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SILLY
You already clicked on that!
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SILLY
You already clicked on that!
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Good Job!
You know your L in FOILDoing good so far!
You’re ready for some practice problems!
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Are you Ready to Practice Problems?
So you think you are ready for some practice problems? Of course you are! Let’s get started.
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The easy One
We’ll start with an easy one.
(x + 3) * (x + 4) = ?
x2 + 12x2 + 3x + 4x + 12
x2 + 7x + 12
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That is Incorrect
That is not the correct answer to(x + 3) * (x + 4)
Remember to use the steps of the FOIL method and also remember to reduce at the end of the
problem.
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Correct!
Good work! The correct answer to(x + 3) * (x + 4)
is in fact x2 + 7x + 12
On to the Next One
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A little bit harder now
This next problem is going to be a bit more difficult, remember to keep track of the signs.
(x + 3) * (x – 4) = ?
x2 – x – 12x2 + 7x – 12
x2 – 12
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That is Incorrect
That is not the correct answer to(x + 3) * (x – 4)
Remember that you have to keep track of the sign because it matters when you are trying to
reduce.
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Correct!
Good work! The correct answer to(x + 3) * (x - 4)
is in fact x2 – x – 12
On to the Next One
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This one is Fun
This is one of the fun ones. Watch the middle term disappear. It is like magic!
(x + 3) * (x – 3) = ?
x2 + 3x – 3x – 9x2 – 9
x2 – 6x – 9
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That is Incorrect
That is not the correct answer to(x + 3) * (x – 3)
Remember that you have to keep track of the sign because it matters when you are trying to
reduce.
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Correct!
Good work! The correct answer to(x + 3) * (x - 3)is in fact x2 – 9
On to the Next One
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Tricky
This one is as tricky as we’ll get.
(x + 3)2 = ?
x2 + 9x2 + 6x + 9
x2 + 3x + 3x + 9
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That is Incorrect
That is not the correct answer to(x + 3)2
This one is a tricky one. Remember that(x + 3)2 = (x + 3) * (x + 3)
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Correct!
Good work! The correct answer to(x + 3)2
is in fact x2 + 6x + 9
Nice Job!
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You Did The Practice Problems!
Good work on those practice problems! You are ready for the quiz now. Good Luck and remember everything you’ve learned!
Quiz Time
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Quiz Time
It is time for the Quiz. It will consist of 10 questions. Remember to simplify your answers and do not forget about the sign each term has
associated with it. Good luck! Please remain quite when you are finished.
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Question 1
(x + 3) * (x + 4) = ?
x2 + 12x2 + 12x + 7x2 + 7x + 12
Incorrect
Sorry to say it, but the answer you selected to the question
(x + 3) * (x + 4) was incorrect. Try again!
Still 10 more to go!
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Correct
Good Job! You answered (x + 3) * (x + 4)
correctly and are that much closer to being done!
9 more to go!
Next
Question 2
(x + 3) * (x – 4) = ?
x2 + 7x – 12x2 + 3x – 4x + 12
x2 – x – 12
Incorrect
Sorry to say it, but the answer you selected to the question
(x + 3) * (x – 4) was incorrect. Try again!
Still 9 more to go!
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Correct
Good Job! You answered (x + 3) * (x – 4)
correctly and are that much closer to being done!
8 more to go!
Next
Question 3
(x – 3) * (x – 4) = ?
x2 + 12x2 – x + 12
x2 – 7x + 12
Incorrect
Sorry to say it, but the answer you selected to the question
(x – 3) * (x – 4) was incorrect. Try again!
Still 8 more to go!
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Correct
Good Job! You answered (x – 3) * (x – 4)
correctly and are that much closer to being done!
7 more to go!
Next
Question 4
(x + 8) * (x + 2) = ?
x2 + 10x + 16x2 + 16x + 10
16x
Incorrect
Sorry to say it, but the answer you selected to the question
(x + 8) * (x + 2) was incorrect. Try again!
Still 7 more to go!
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Correct
Good Job! You answered (x + 8) * (x + 2)
correctly and are that much closer to being done!
6 more to go!
Next
Question 5
(x + 7)2 = ?
x2 + 49x2 + 49x + 49x2 + 14x + 49
Incorrect
Sorry to say it, but the answer you selected to the question
(x + 7)2
was incorrect. Try again!
Still 6 more to go!
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Correct
Good Job! You answered (x + 7)2
correctly and are that much closer to being done!
5 more to go!
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Question 6
(x – 7)2 = ?
x2 – 14x + 49x2 – 14x + 56
x2 + 49
Incorrect
Sorry to say it, but the answer you selected to the question
(x – 7)2
was incorrect. Try again!
Still 5 more to go!
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Correct
Good Job! You answered (x – 7)2
correctly and are that much closer to being done!
4 more to go!
Next
Question 7
(x – 6) * (x + 0) = ?
x2 – 6x – 6x2 – 0x – 6
x2 – 6x
Incorrect
Sorry to say it, but the answer you selected to the question
(x – 6) * (x + 0) was incorrect. Try again!
Still 4 more to go!
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Correct
Good Job! You answered (x – 6) * (x + 0)
correctly and are that much closer to being done!
3 more to go!
Next
Question 8
(x – 6) * (x + 6) = ?
x2 – 6x + 6x – 36x2 – 36x2 + 36
Incorrect
Sorry to say it, but the answer you selected to the question
(x – 6) * (x + 6) was incorrect. Try again!
Still 3 more to go!
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Correct
Good Job! You answered (x – 6) * (x + 6)
correctly and are that much closer to being done!
2 more to go!
Next
Question 9
(x + 2) * (x – 2) = ?
x2 – 4x2 + 2x – 4x2 +2x + 4
Incorrect
Sorry to say it, but the answer you selected to the question
(x + 2) * (x – 2) was incorrect. Try again!
Still 2 more to go!
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Correct
Good Job! You answered (x + 2) * (x – 2)
correctly and are that much closer to being done!
1 more to go!
Next
Question 10
(x – 1)2 = ?
x2 – 1x2 + 1
x2 – 2x + 1
Incorrect
Sorry to say it, but the answer you selected to the question
(x – 1)2
was incorrect. Try again!
Still 1 more to go!
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Congratulations!
Congrats! You answered all of the questions on the quiz correctly. Feel free to go back through
this program if you wish!
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