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

2. 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

3. 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.

4. 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

5. 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

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

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

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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

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

22. Last Home

23. Practice Practice Understanding FOIL Practice Problems Main Menu

24. 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

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

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

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

28. SILLY You already clicked on that! Last Home

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

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

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

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

33. SILLY You already clicked on that! Last Home

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

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

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

37. 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

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

39. That is Correct! The O in FOIL stands for Outer! Good Job! Now click on the outer terms. (x + 3) * (x + 4) Home

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

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

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

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

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

45. SILLY You already clicked on that! Last Home

46. SILLY You already clicked on that! Last Home

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

48. 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

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

50. That is Correct! The I in FOIL stands for Inner! Good Job! Now click on the inner terms. (x + 3) * (x + 4) Home

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

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

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

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

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

56. SILLY You already clicked on that! Last Home

57. SILLY You already clicked on that! Last Home

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

59. 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

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

61. That is Correct! The L in FOIL stands for Last! Good Job! Now click on the last terms. (x + 3) * (x + 4) Home

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

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

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

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

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

67. SILLY You already clicked on that! Last Home

68. SILLY You already clicked on that! Last Home

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

70. 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

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

72. 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

73. 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

74. 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

75. 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

76. 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

77. 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

78. 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

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

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

81. 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

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

83. 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

84. 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

85. Question 1 (x + 3) * (x + 4) = ? x 2 + 12 x 2 + 12x + 7 x 2 + 7x + 12

86. 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

87. Correct Good Job! You answered (x + 3) * (x + 4) correctly and are that much closer to being done! 9 more to go! Next

88. Question 2 (x + 3) * (x – 4) = ? x 2 + 7x – 12 x 2 + 3x – 4x + 12 x 2 – x – 12

89. 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

90. Correct Good Job! You answered (x + 3) * (x – 4) correctly and are that much closer to being done! 8 more to go! Next

91. Question 3 (x – 3) * (x – 4) = ? x 2 + 12 x 2 – x + 12 x 2 – 7x + 12

92. 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

93. Correct Good Job! You answered (x – 3) * (x – 4) correctly and are that much closer to being done! 7 more to go! Next

94. Question 4 (x + 8) * (x + 2) = ? x 2 + 10x + 16 x 2 + 16x + 10 16x

95. 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

96. Correct Good Job! You answered (x + 8) * (x + 2) correctly and are that much closer to being done! 6 more to go! Next

97. Question 5 (x + 7) 2 = ? x 2 + 49 x 2 + 49x + 49 x 2 + 14x + 49

98. 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

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

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

101. 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

102. Correct Good Job! You answered (x – 7) 2 correctly and are that much closer to being done! 4 more to go! Next

103. Question 7 (x – 6) * (x + 0) = ? x 2 – 6x – 6 x 2 – 0x – 6 x 2 – 6x

104. 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

105. Correct Good Job! You answered (x – 6) * (x + 0) correctly and are that much closer to being done! 3 more to go! Next

106. Question 8 (x – 6) * (x + 6) = ? x 2 – 6x + 6x – 36 x 2 – 36 x 2 + 36

107. 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

108. Correct Good Job! You answered (x – 6) * (x + 6) correctly and are that much closer to being done! 2 more to go! Next

109. Question 9 (x + 2) * (x – 2) = ? x 2 – 4 x 2 + 2x – 4 x 2 +2x + 4

110. 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

111. Correct Good Job! You answered (x + 2) * (x – 2) correctly and are that much closer to being done! 1 more to go! Next

112. Question 10 (x – 1) 2 = ? x 2 – 1 x 2 + 1 x 2 – 2x + 1

113. 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

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