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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
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
How to FOIL?
Take the binomial (a+b) and multiply it by (c+d)
So it would look like this in a question:
In this case the first (F) is considered the a and the c because they are the first numbers in the either binomial.
The outers (O) is considered the a and the d because they are the outside numbers when the equation is shown
The inners (I) are the b and the c because they are the inside numbers
And finally the Lasts (L) are the b and the d because they are the last numbers of each binomial
Exit (Cont. on next slide)
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
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
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
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
Test Time! Exit
Q. 1 what does FOIL stand for?
First outers inners last
Front outside inside lopsided
Frustrated, overworked, insignificant, lazy
Q. 2 what operation do you perform between each letter of foil?
Q. 3 what is (x + y)(x + y)?
I’m going to go through these slides again!
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
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