Welcome to the F.O.I.L. method! Let’s Get Started! Next

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. Next

How to Navigate this Program Next 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 Next The following arrow will also be seen on most screens and when clicked on will take you to the previous page. It will be located in the lower left-hand corner. You can go ahead and click on it to try it out if you haven’t already. Last

How to Navigate this Program Next 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. Last

Button Help Next Screen Previous Screen Home Most recent selection menu Help Screen (current page) Last

Button Help Next Screen Previous Screen Home Most recent selection menu Help Screen (current page)

Button Help Next Screen Previous Screen Home Most recent selection menu Help Screen (current page)

How to Navigate this Program Next 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. Last Home

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. Next Home

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, x 2 – 1, x + 18, x + 5, –8 + 7x Next Last Home

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: First Outer Inner Last Home Next

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 Next Home

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 = x 2 Next Last Home

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 Next Last Home

We’re Halfway Done We have gotten halfway through FOIL so make sure you understand why we currently have: x 2 + 4x If you are unsure how we got this make sure you go back and review a little bit. Next Last Home

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 x 2 + 4x + 3x Next Last Home

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 x 2 + 3x + 4x +12 But wait! There is more! Next Last Home

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. x 2 + 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 Next Last Home

Click next to see more problems worked out. Last Home Next x 2 + 7x +12

Last Home

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? Famous First Friend Freak Home

You Guessed Wrong! That is not what the F in FOIL stands for! Review the FOIL method if you forget. Last Home

That is Correct! The F in FOIL stands for First! Good Job! Now click on the first terms. (x + 3) * (x + 4) Home

That is Correct! Now Click the other First term (x + 3) * (x + 4) Home

SILLY You already clicked on that! Last Home

Good Job! You know your F in FOIL Doing good so far! Next Home

That is Correct! Now Click the other First term (x + 3) * (x + 4) Home

Incorrect That is not one of the first terms. Go back and Review Last Home

That is Correct! Now Click the other First term (x + 3) * (x + 4) Home

SILLY You already clicked on that! Last Home

Good Job! You know your F in FOIL Doing good so far! Next Home

Incorrect That is not one of the first terms. Go back and Review Last Home

Incorrect That is not one of the first terms. Go back and Review Last Home

So Let’s Make Sure We Know What FOIL Means The O in FOIL stands for which of the following? Outer Omit Odd Oops Home

You Guessed Wrong! That is not what the O in FOIL stands for! Review the FOIL method if you forget. Last Home

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 Last Home

Incorrect That is not one of the outer terms. Go back and Review Last Home

Incorrect That is not one of the outer terms. Go back and Review Last Home

SILLY You already clicked on that! Last Home

SILLY You already clicked on that! Last Home

Good Job! You know your O in FOIL Doing good so far! Next Home

So Let’s Make Sure We Know What FOIL Means The I in FOIL stands for which of the following? IDK Indeed Inner Imagine Home

You Guessed Wrong! That is not what the I in FOIL stands for! Review the FOIL method if you forget. Last Home

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) Home

Incorrect That is not one of the Inner terms. Go back and Review Last Home

Incorrect That is not one of the Inner terms. Go back and Review Last Home

Incorrect That is not one of the Inner terms. Go back and Review Last Home

SILLY You already clicked on that! Last Home

SILLY You already clicked on that! Last Home

Good Job! You know your I in FOIL Doing good so far! Next Home

So Let’s Make Sure We Know What FOIL Means The L in FOIL stands for which of the following? Lame Left Last Lucky Home

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) Home

Incorrect That is not one of the Last terms. Go back and Review Last Home

Incorrect That is not one of the Last terms. Go back and Review Last Home

Incorrect That is not one of the Last terms. Go back and Review Last Home

SILLY You already clicked on that! Last Home

SILLY You already clicked on that! Last Home

Good Job! You know your L in FOIL Doing good so far! You’re ready for some practice problems! Next Home

Are you Ready to Practice Problems? So you think you are ready for some practice problems? Of course you are! Let’s get started. Next Home

The easy One We’ll start with an easy one. (x + 3) * (x + 4) = ? x x 2 + 3x + 4x + 12 x 2 + 7x + 12 Home

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. Last Home

Correct! Good work! The correct answer to (x + 3) * (x + 4) is in fact x 2 + 7x + 12 On to the Next One Next Home

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) = ? x 2 – x – 12 x 2 + 7x – 12 x 2 – 12 Home

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. Last Home

Correct! Good work! The correct answer to (x + 3) * (x - 4) is in fact x 2 – x – 12 On to the Next One Next Home

This one is Fun This is one of the fun ones. Watch the middle term disappear. It is like magic! (x + 3) * (x – 3) = ? x 2 + 3x – 3x – 9 x 2 – 9 x 2 – 6x – 9 Home

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. Last Home

Correct! Good work! The correct answer to (x + 3) * (x - 3) is in fact x 2 – 9 On to the Next One Next Home

Tricky This one is as tricky as we’ll get. (x + 3) 2 = ? x x 2 + 6x + 9 x 2 + 3x + 3x + 9 Home

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) Last Home

Correct! Good work! The correct answer to (x + 3) 2 is in fact x 2 + 6x + 9 Nice Job! Next Home

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 Home

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. Next Home

Question 1 (x + 3) * (x + 4) = ? x x x + 7 x 2 + 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! Last

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) = ? x 2 + 7x – 12 x 2 + 3x – 4x + 12 x 2 – 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! Last

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) = ? x x 2 – x + 12 x 2 – 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! Last

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) = ? x x + 16 x x x

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! Last

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 = ? x x x + 49 x x + 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! Last

Correct Good Job! You answered (x + 7) 2 correctly and are that much closer to being done! 5 more to go! Next

Question 6 (x – 7) 2 = ? x 2 – 14x + 49 x 2 – 14x + 56 x

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! Last

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) = ? x 2 – 6x – 6 x 2 – 0x – 6 x 2 – 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! Last

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) = ? x 2 – 6x + 6x – 36 x 2 – 36 x

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! Last

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) = ? x 2 – 4 x 2 + 2x – 4 x 2 +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! Last

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 = ? x 2 – 1 x x 2 – 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! Last

Congratulations! Congrats! You answered all of the questions on the quiz correctly. Feel free to go back through this program if you wish! Home