This document discusses the FOIL method for multiplying binomial expressions. It begins by defining polynomials and binomials. It then explains that FOIL stands for First, Outer, Inner, Last - the steps to multiply the terms of two binomials. Several example problems are worked out using FOIL, including the bonus question of multiplying two polynomials. Homework is assigned practicing FOIL on selected problems from the textbook.

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. SOLUTIONS
Hmmm . .
 Problem #1 ..
 Problem #2
 Problem #3
 Problem #4
 Problem #5
 Bonus Question

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. 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. 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. 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. 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. 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. 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. 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. 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 