The document provides an explanation of how to use the FOIL method to multiply binomial expressions. It defines what a binomial is, explains that FOIL is a mnemonic for the steps of First, Outer, Inner, Last. It then demonstrates how to use FOIL by working through simple examples without variables and a more complex example with variables, showing the pairing and multiplication of terms according to the FOIL steps. Additional resources on FOIL multiplication are provided.

1. Using Foil to Multiply Binomials By Ed Harris Ed 205

3. What is a binomial? A binomial is an expression that consists of a sum or a difference of 2 numeric values For example: (3+2) (6-1) (10x+2) (7-4y) (10x-4y) Are all binomials because there are 2 numeric values enclosed in parenthesis. These are not binomials: 3 (monomial) 3+4x+7y (trinomial) Exit

4. What is FOIL? FOIL is a shortcut to multiplying binomials. FOIL is an alliteration for the steps involved as shown below and on the next slide: Foil stands for F irst O uters I nners L ast These may not make sense now but these are the steps on how to multiply binomials and it will become more clear on the next slide. Exit

6. How to FOIL? Cont. So F =a x c, O =a x d, I =b x c and L =b x d Notice that the pairing given by foil are multiplied. Now if we were to add all of these products we would get the answer to (a+b)(c+d) In other words what foil really means is: (a x c)+(a x d)+(b x c)+(b x d) Still confused? In the next slides we will show some examples with real numbers that may clear things up. Exit

7. Simple example (no variables) Ex. (3+5)(4+2) Solution: F irst: 3 x 4 O utters: 3 x 2 I nners: 5 x 4 L ast: 5 x 2 Add these together and you get: (3 x 4)+(3 x 2)+(5 x 4)+(5 x 2) = 12 + 6 + 20 + 10 = 48 With a problem like this you can also solve this with order of operation so lets see how that works: 3+5=8 and 4+2=6 8 x 6 = 48 which checks out! Exit

8. Complex example (w/ variables) Ex. (6x-3y)(x+y) *note* because there is unlike variables inside the parenthesis order of operation can not be used F irst: 6x x x O uters: 6x x y I nners: -3y x x L asts: -3y x y Add these together and you get: (6x x x)+(6x x y)+(-3y x x)+(-3y x y) = 6x^2 + 6xy + -3xy + -3y^2 = 6x^2-3y^2+3xy *note* the x^2 and y^2 have nothing to add together with so they stay as they are but the xy can be put together. Exit

9. Still Unsure? If you have read my bio you would know that I am not a math teacher yet so if I have not done a good enough job of explaining please check out this video and maybe some professionals will be able to fill in the gaps! Watch a real teacher show you how to do it! Exit

11. WRONG!!!!!!!

12. CORRECT!!!!!

13. References Exit Youtube video showing how to multipy binomials http://video.google.com/videoplay?docid=-1472605947635291271&q=foil+multiplication&ei=zvVCSNjQEZzQ4gKu9dXtCA&hl=en Foil http://id.mind.net/~zona/mmts/miscellaneousMath/expressionsWithParentheses/foil1.html

14. About the author Ed Harris is a student at gvsu currently going for his math degree to teach middle school math. He is 21 years of age and lives in Jenison, Mi where he has resided for over 3 years now.Ed is a marathon runner in his free time and loves hockey. If you would like to contact Ed e-mail him at [email_address] Exit

15. Concept Map Exit