using foil to multiply binomials
DESCRIPTION
my ppt presentation on multiplying binomials.TRANSCRIPT
![Page 1: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/1.jpg)
Using Foil to Multiply Binomials
By Ed Harris
Ed 205
![Page 2: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/2.jpg)
Main page• What is a binomial• What is foil• How to foil• Simple examples (no variables)• Complex examples• Still unsure?• Test time!• References• About the author• Concept map
![Page 3: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/3.jpg)
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
![Page 4: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/4.jpg)
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 forFirstOutersInnersLast
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
![Page 5: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/5.jpg)
How to FOIL?Take the binomial (a+b) and multiply it by (c+d)So it would look like this in a question:
(a+b)(c+d)=?
•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)
![Page 6: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/6.jpg)
How to FOIL? Cont.So F=a x c, O=a x d, I=b x c and L=b x dNotice 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
![Page 7: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/7.jpg)
Simple example (no variables)
Ex. (3+5)(4+2)
Solution:First: 3 x 4Outters: 3 x 2Inners: 5 x 4Last: 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=68 x 6 = 48 which checks out!
Exit
![Page 8: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/8.jpg)
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
First: 6x x xOuters: 6x x yInners: -3y x xLasts: -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
![Page 9: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/9.jpg)
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
![Page 10: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/10.jpg)
Test Time!
Exit
Q. 1 what does FOIL stand for?A) First outers inners lastB) Front outside inside lopsidedC) Frustrated, overworked, insignificant, lazyQ. 2 what operation do you perform between each letter of foil?A) addition/subtractionB) Multiplication/divisionC) E=mc2Q. 3 what is (x + y)(x + y)?A) x^2-y^2B) x^2+y^2+2xyC) I’m going to go through these slides again!
![Page 11: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/11.jpg)
WRONG!!!!!!!
![Page 12: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/12.jpg)
CORRECT!!!!!
![Page 13: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/13.jpg)
References
Exit
Youtube video showing how to multipy binomialshttp://video.google.com/videoplay?docid=-1472605947635291271&q=foil+multiplication&ei=zvVCSNjQEZzQ4gKu9dXtCA&hl=en
Foilhttp://id.mind.net/~zona/mmts/miscellaneousMath/expressionsWithParentheses/foil1.html
![Page 14: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/14.jpg)
About the authorEd 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 [email protected]
Exit
![Page 15: Using Foil To Multiply Binomials](https://reader034.vdocuments.us/reader034/viewer/2022042509/555ae36cd8b42a62528b53ca/html5/thumbnails/15.jpg)
Concept Map
Exit