The F.O.I.L. Method

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The F.O.I.L. Method
(ab)(cd)
(2x3)(4x2)
(z-1)(y-6)

• An Algebra Lesson

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Lesson Objectives

• In todays lesson, we will expand on what you
  already know about binomials.
• You will soon be able to accurately multiply
  binomials using a new method, called the F.O.I.L.
  method.

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Orientation

• In todays algebra lesson, we will use
  multiplication skills and our knowledge of
  binomials to multiply two binomials together.
• Throughout the rest of this lesson, you should
  click on the appropriate green buttons to
  navigate. Start at the main menu and start with
  key terms, then motivation, etc. You will be
  evaluated with a quiz at the end of the lesson.

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Main Menu
Learning the F.O.I.L. Method
Key Terms
Application
Motivation
Quiz
The F.O.I.L. Method
Please click on the appropriate buttons to
navigate through the lessons. Click on the home
button to come back to the Main Menu.
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Key Terms

• In order to learn a new algebra lesson, it is
  important for you to know several key terms.

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Monomial-

• An algebraic expression that contains only one
  term.

Examples
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Examples of Monomials

• a
• -7x2
• 2/3y

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Binomial-

• An algebraic expression that contains two unlike
  terms.

Examples
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Examples of Binomials

• 32a
• x²-y²
• 2x²3y³

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Polynomial-

• An algebraic expression that contains two or more
  unlike terms.

Examples
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Examples of Polynomials

• a² b c
• 3x 2y
• 5a 2b³ 3c²

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Parentheses

• Indicate multiplication.

(2x)(3) This means to multiply the two monomials
together.
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Motivation

• The F.O.I.L. Method will help you continue your
  success in algebra!

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Motivation

• Since you know how to multiply and you know what
  a binomial is, you should be able to handle the
  F.O.I.L. method!

Ready to start learning?
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What is the F.O.I.L. Method??
Find out!!!
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• The F.O.I.L. Method is a method used to multiply
  tow binomials together.
• (3x 2)(4x 7)

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What does F.O.I.L. stand for???
Find out!
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F.O.I.L.

• F- First, multiply the first term in each set of
  parenthesis.
• O- Next, multiply the two terms on the outside.
• I-Then, multiply the two inside terms.
• L- Last, multiply the last terms in each
  binomial.

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Helpful Advice

• What do you do after you have multiplied the
  terms?
• You add together like terms, if possible.

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• Lets look at some example problems. See if you
  get the same answers, by working out the problems
  on a separate sheet of paper.

Problem 3
Problem 1
Problem 2
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Problem 1

• (3x 2)(6x 1) ?
• 18x² 3x 12x 2
• 18x² 15x 2 FINAL ANSWER

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Problem 2

• (-4 a)(b 2) ?
• -4b 8 ab 2a FINAL ANSWER
• -2a 4b ab 8 (rewritten)

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Problem 3

• (x 3) (x² 5) ?
• x³ 5x 3x² 15
• x³ 3x² 5x 15 FINAL ANSWER

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• Now, lets see if you can do the F.O.I.L. method
  by yourself!

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Problem

• ( 10a b²) ( 3 2a) ?
• Work out the problem on a piece of paper. Click
  the next button after you have solved the problem.

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Answer

• (10a b²) (3 2a) ?
• 30a 20a² 3b² 2ab²
• Hope you got the right answer!

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Lets try one more!

• Problem
• (-z 8) (y 1) ?

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Answer

• (-z 8) (y 1) ?
• -zy z 8y 8
• Good effort!
• Now that you understand the F.O.I.L. method,
  its time to take the quiz!

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Youve done great so far! Keep up the hard work
on this quiz!

• Quiz Directions
• There are ten problems.
• Work them out on paper and click a corresponding
  answer button.
• Good luck!

Start Quiz!
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• Problem 1
• (x 4) (x 2) ?

• Possible Answers

x² - 2x - 8
-x² 2x - 6
x³ x² x
x² 2x 8
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x² 2x 8 CORRECT!!!!
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Try again!
Remember F.O.I.L.
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• Problem 2
• What does F.O.I.L. stand for?

• Possible Answers

First, Outside, Inside, Last
Factor Out Inside Letters
Find Or Investigate the Long (equation)
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First, Outside, Inside, LastYou got it!!!
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Think! You know this!
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• Problem 3
• What does the F.O.I.L. method multiply?

• Possible Answers

Square Roots
Exponents
Binomials
Line Segments
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Binomials!Good Answer!
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Not quitegive it another shot!
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• Problem 4
• (a b) (7 2b) ?

• Possible Answers

-5ab 5b²
7a 7b 2b²
7ab b 2b²
-2b² 7a 2ab 7
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-2b² 7a - 2ab 7 Wow! Way to go!
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Oops! Check your work again!
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• Problem 5
• (3 x) (10 y) ?

• Possible Answers

xy 10x 3y 30
-xy 3x 10y 30
30xy 3x 3y
xy 10x 3y 30
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xy 10x 3y 30

• Yeah! You are awesome!

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Nope, try again!F.O.I.L.
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• Problem 6
• (x 3x²) (x 2) ?

• Possible Answers

3x³ 7x² 2x
9x² x 2
6x² 2x 3
x³ 5x² 2x
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3x³ 7x² 2xCorrect! Almost done!
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Try to F.O.I.L. the problem again! Dont give up!
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• Problem 7
• (2 a) (3 b²) ?

• Possible Answers

6b² 6a - 3
-ab² 2b² - 3a 6
ab² 5b² - 6
-ab² - 2b² 3a - 5
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-ab² 2b² - 3a 6Keep up the great work!
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You know the F.O.I.L. method! Maybe you made a
small mistaketry again!
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• Problem 8
• What do you do after you have multiplied the
  binomials?

• Possible Answers

Combine like terms, if possible.
Multiply again.
Use the F.O.I.L. method.
You never multiply binomials.
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Combine like terms, if possible!Super Job!
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No, try to remember what you learned earlier in
the lesson.
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• Problem 9
• (-x 1) (x 4) ?

• Possible Answers

-2x - 4
-x 4
-x² - 5x 4
-x² 3x 4
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-x² 3x 4Fantastic!
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Try again! Youll get it!
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• Problem 10
• (x² - x) (5x 6) ?

• Possible Answers

5x³ x² - 6
4x² 11x - 6
Last problem!
5x³ - x² 6
4x² - 11x 6
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5x³ x² - 6 Congrats! You have finished the
quiz!!!
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Oh, come on! This is your last problem! Give it
all you got!
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Check how many problems you got right on the
first try

• 10 correct- You did an amazing job! Congrats on
  conquering the F.O.I.L. method!
• 8 correct- Nicely done! You have successfully
  learned how to foil.
• Less than 8 correct- Keep trying. You may want to
  look over the lesson again.

Click here if you are done with the lesson.
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Thanks for trying so hard today! You did great!
Good luck with using the F.O.I.L. method in the
future!
Works Cited
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Works Cited

• Microsoft ClipArt
• Smiling Man- An Educators Reference Desk Lesson
  Plan (1999, May 31). lthttp//eduref.org/Virtual/L
  essons/Mathematics/Algebra/ALG0003.htmlgt.