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)
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?
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
For example, x2 - 5x + 6 and 2p3q + y are
WHAT IS A BINOMIAL?
Algebra. an expression that is a sum or difference
of two terms.
Some examples are: 3x + 2y and x2 − 4x
CAN ANYONE COME UP WITH SOME OTHER
( + )( - )
YOU INSERT YOUR OWN NUMBERS
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
Don’t forget what
foil stands for!
WHAT IS THE FOIL DANCE?
F – First
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!
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.
SOME EXAMPLE PROBLEMS TO WORK ON:
Hmmm . .
Problem #1 ..
PROBLEM #1 - SOLUTION
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
PROBLEM #2 - SOLUTION
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
PROBLEM #3 - SOLUTION
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
PROBLEM #4 - SOLUTION
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
PROBLEM #5 - SOLUTION
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
DUE AT THE BEGINNING OF NEXT CLASS
From the textbook:
# 1-8, 10-24 (even problems only), 33, 35, 47
We have talked about multiplying BINOMIALS, but
what happens when we multiply polynomials?
PLEASE SHOW ALL OF YOUR WORK!
ANSWER TO BONUS QUESTION
(TO BE SHOWN AT THE BEGINNING OF NEXT CLASS)
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
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