THE FOIL METHOD




              BY: MARY C. LENT

     Satisfies grade level content expectations:
A.F0.07.12 – add, sub...
WHAT WOULD YOU LIKE TO LEARN?
 What is a polynomial?
 What is a binomial?
 What are some examples of binomials?
 What ...
WHAT IS A POLYNOMIAL?
 An algebraic expression consisting of one or more
  summed terms, each term consisting of a consta...
WHAT IS A BINOMIAL?
 Algebra. an expression that is a sum or difference
  of two terms.
 Some examples are: 3x + 2y and ...
CAN ANYONE COME UP WITH SOME OTHER
            EXAMPLES?

   (x+6)(x+10)

   (x-5)(x+2)

   (x^2+1)(x+7)

   (x^2+2)(x...
WHAT DOES FOIL STAND FOR?




 F: multiply the FIRST terms
 O: multiply the OUTER terms

 I: multiply the INNER terms

...
Don’t forget what

                                                                     foil stands for!




             ...
DO YOU KNOW HOW TO DANCE?


Its your turn now!!!
Show me your moves!



 There are stations set up on the whiteboard, and
...
ITS VOLUNTEER TIME!
   I need 5 volunteers to make up binomials and write
    them on the board.




   I also need 5 vo...
SOME EXAMPLE PROBLEMS TO WORK ON:
1)   (x-3)(x+2)

2)   (x^2+6)(x+1)

3)   (2x+5)(x+9)

4)   (x^2+4)(x^2+7)

5)   (x-10)(x...
SOLUTIONS
                                 Hmmm . .
   Problem #1                     ..


   Problem #2

   Problem #3...
PROBLEM #1 - SOLUTION
                          FOIL

                         (x-3)(x+2)

First: (x)(x) = x^2
Outer: (x)(...
PROBLEM #2 - SOLUTION
                          FOIL

                        (x^2+6)(x+1)

First: (x^2)(x) = x^3
Outer: (...
PROBLEM #3 - SOLUTION
                            FOIL

                         (2x+5)(x+9)

First: (2x)(x) = 2x^2
Outer:...
PROBLEM #4 - SOLUTION
                             FOIL

                          (x^2+4)(x^2+7)

First: (x^2)(x^2) = x^4...
PROBLEM #5 - SOLUTION
                          FOIL

                         (x-10)(x-8)

First: (x)(x) = x^2
Outer: (x)...
HOMEWORK
     DUE AT THE BEGINNING OF NEXT CLASS
   From the textbook:
    Pages 81-82
    # 1-8, 10-24 (even problems on...
Bonus
                       Question




We have talked about multiplying BINOMIALS, but
 what happens when we multiply p...
ANSWER TO BONUS QUESTION
(TO BE SHOWN AT THE BEGINNING OF NEXT CLASS)
                  (x-6)(x^2+16x+72)
Steps 1) (x)(x^2...
THANK YOU



I would like to thank TeacherTube.com for the
  delightful FOIL video

Thank you to Google Images for all of ...
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Ed 205 Foil

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Ed 205 Foil

  1. 1. THE FOIL METHOD BY: MARY C. LENT Satisfies grade level content expectations: A.F0.07.12 – add, subtract, MULTIPLY simple algebraic expressions of the first degree and justify using properties of real numbers (7th – 8th graders)
  2. 2. WHAT WOULD YOU LIKE TO LEARN?  What is a polynomial?  What is a binomial?  What are some examples of binomials?  What does FOIL stand for?  What is the FOIL dance?  Do you know how to dance?  Who would like to volunteer?  What are some example problems?  What are the solutions?  What is the homework assignment tonight?  What is the BONUS question?
  3. 3. WHAT IS A POLYNOMIAL?  An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers.  For example, x2 - 5x + 6 and 2p3q + y are polynomials.
  4. 4. WHAT IS A BINOMIAL?  Algebra. an expression that is a sum or difference of two terms.  Some examples are: 3x + 2y and x2 − 4x
  5. 5. CAN ANYONE COME UP WITH SOME OTHER EXAMPLES?  (x+6)(x+10)  (x-5)(x+2)  (x^2+1)(x+7)  (x^2+2)(x^2-3)  ( + )( - ) YOU INSERT YOUR OWN NUMBERS 
  6. 6. WHAT DOES FOIL STAND FOR?  F: multiply the FIRST terms  O: multiply the OUTER terms  I: multiply the INNER terms  L: multiply the LAST terms
  7. 7. Don’t forget what foil stands for! WHAT IS THE FOIL DANCE? F – First O- Outer I- Inner L- Last http://www.teachertube.com/view_video.ph p?viewkey=2eed5c6ddbee10e6ea94
  8. 8. DO YOU KNOW HOW TO DANCE? Its your turn now!!! Show me your moves! There are stations set up on the whiteboard, and there are stations set up on the floor. Please go to four stations before you sit back down and make sure the people around you understand it as well!
  9. 9. ITS VOLUNTEER TIME!  I need 5 volunteers to make up binomials and write them on the board.  I also need 5 volunteers to try and solve them using the FOIL method we just discussed.
  10. 10. SOME EXAMPLE PROBLEMS TO WORK ON: 1) (x-3)(x+2) 2) (x^2+6)(x+1) 3) (2x+5)(x+9) 4) (x^2+4)(x^2+7) 5) (x-10)(x-8)
  11. 11. SOLUTIONS Hmmm . .  Problem #1 ..  Problem #2  Problem #3  Problem #4  Problem #5  Bonus Question
  12. 12. PROBLEM #1 - SOLUTION FOIL (x-3)(x+2) First: (x)(x) = x^2 Outer: (x)(2) = 2x Inner: (-3)(x) = -3x Last: (-3)(2) = -6 x^2+2x+-3x+-6 If necessary, simplify by adding like terms ANSWER: x^2-x-6
  13. 13. PROBLEM #2 - SOLUTION FOIL (x^2+6)(x+1) First: (x^2)(x) = x^3 Outer: (x^2)(1) = x^2 Inner: (6)(x) = 6x Last: (6)(1) = 6 x^3+x^2+6x+6 If necessary, simplify by adding like terms ANSWER: x^3+x^2+6x+6
  14. 14. PROBLEM #3 - SOLUTION FOIL (2x+5)(x+9) First: (2x)(x) = 2x^2 Outer: (2x)(9) = 18x Inner: (5)(x) = 5x Last: (5)(9) = 45 2x^2+18x+5x+45 If necessary, simplify by adding like terms ANSWER: 2x^2+23x+45
  15. 15. PROBLEM #4 - SOLUTION FOIL (x^2+4)(x^2+7) First: (x^2)(x^2) = x^4 Outer: (x^2)(7) = 7x^2 Inner: (4)(x^2) = 4x^2 Last: (4)(7) = 28 x^4+7x^2+4x^2+28 If necessary, simplify by adding like terms ANSWER: x^4+11x^2+28
  16. 16. PROBLEM #5 - SOLUTION FOIL (x-10)(x-8) First: (x)(x) = x^2 Outer: (x)(-8) = -8x Inner: (-10)(x) = -10x Last: (-10)(-8) = 80 x^2+-8x+-10x+80 If necessary, simplify by adding like terms ANSWER: x^2+-18x+80
  17. 17. HOMEWORK DUE AT THE BEGINNING OF NEXT CLASS  From the textbook: Pages 81-82 # 1-8, 10-24 (even problems only), 33, 35, 47
  18. 18. Bonus Question We have talked about multiplying BINOMIALS, but what happens when we multiply polynomials? (x-6)(x^2+16x+72) PLEASE SHOW ALL OF YOUR WORK!
  19. 19. ANSWER TO BONUS QUESTION (TO BE SHOWN AT THE BEGINNING OF NEXT CLASS) (x-6)(x^2+16x+72) Steps 1) (x)(x^2) = x^3 2) (x)(16x) = 16x^2 3) (x)(72) = 72x 4) (-6)(x^2) = -6x^2 5) (-6)(16x) = -96x 6) (-6)(72) = -432 X^3+16x^2+72x+-6x^2+-96x+-432 Simplify if needed ANSWER: x^3+10x^2-14x-432
  20. 20. THANK YOU I would like to thank TeacherTube.com for the delightful FOIL video Thank you to Google Images for all of the pictures that were included Special Thanks to Professor LaBeau – I really enjoyed this project 

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