Math Is Fun Forum

blank_brunette

Member

Registered: 2008-03-27

Posts: 46

Foil

hi...im having a little trouble with this thing called the foil method. can anyone explain it to me? and anything else you can tell me about the distributive property?

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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Foil

"Firsts, Outers, Inners, Lasts": Multiplying Polynomials (part way down)

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bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Foil

The FOIL page that MathsIsFun should cover what you need to know, but in case it doesn't, I'll express it the way I like to think of it.

I sometimes like to think about the distributive property visually. Pretend you have a bunch of oranges:

Now if you want to find out how many oranges you have, you can count how many there are vertically (in this case there are (3+2) and multiply that by how many there are horizontally (4)

4*(3+2)=20

Suppose instead you break it into two groups (they can be of equal size if you want, but don't have to be). In this case, the top group is 4 by 3 and the bottom group is 4 by 2. If you add the two groups together it's apparent that you will get the total amount of oranges:

4*3 + 4*2 = 20

In this example, you can clearly see that:

4*(3+2) = 4*3+4*2

You should be able to convince yourself of a general rule:

a(b+c) = ab+ac

Got that down? Alright, let's FOIL.

To "see" why FOIL works, we're going to do some algebra. We want to know what

(a+b)*(c+d)

is when multiplied out. To do that we're going to make a substitution. Trust me on this, we're going to say:

u = (a+b)

and now we can substitute our newly defined variable into the original:

(a+b)*(c+d) = u*(c+d)

Using the distributive property (that we now know and love):

u*(c+d) = uc+ud

Subbing u=(a+b)  back into the equation we get:

uc+ud = (a+b)*c + (a+b)*d

And using th distributive property again, we get:

(a+b)*c + (a+b)*d = ac + bc + ad + bd

So ultimately we see that:

(a+b)(c+d) = ac + ad + bc+ bd

Which is FOIL: Firsts (ac) Outers (ad) Inners (bc) Lasts (bd).

Cool?

Last edited by bossk171 (2008-05-01 15:02:21)

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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Foil

Neat.

You could use even more oranges to show something like (2+3)(4+5)

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blank_brunette

Member

Registered: 2008-03-27

Posts: 46

Re: Foil

wow--------i got a headache, but thanx so much! if you have anything to add, please do!

Last edited by blank_brunette (2008-05-02 07:33:54)

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blank_brunette

Member

Registered: 2008-03-27

Posts: 46

Re: Foil

ok, i have a question.....my hw is giving me an equation and it says to find the line of symmetry and the x and y intercept and min and max point. Plus, lets just say that I was distracted in class today,:/ so i dont know how to do it. My problem is  y= (x-3)(x=3)
What do I do????

Last edited by blank_brunette (2008-05-06 12:50:44)

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simron

Real Member

Registered: 2006-10-07

Posts: 237

Re: Foil

I'm assuming that the x=3 thing was a typo and that you really meant y=(x-3)(x+3). It's a common error.
Here are the steps:
-Find the vertex. On parabolas, if the vertex is at (a,b), then the line of symmetry is at x=b.
-Set x and y equal to 0 and represent that as a point. Those are your x and y-intercepts.
-Minimum and maximum points: The best thing to do is to graph it. One special property of parabolas is that they cannot have a minimum and a maximum point. If you don't want to do that and you are in Calculus, just take the derivative and set it equal to 0.
Hope this helps!

Last edited by simron (2008-05-06 14:44:55)

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Foil

This is quite a nice one to find the line of symmetry for. As simron said, to find the line of symmetry you need to find the vertex. In this case, doing that isn't very hard.

Using the FOIL method to expand the brackets gives (x-3)(x+3) = x² -3x +3x -9 = x² - 9.
(The middle two terms cancel each other)

x² is non-negative for any real value of x, and so the lowest it can be is 0 (which happens when x=0). Therefore, the vertex of this parabola is at (0,-9).

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blank_brunette

Member

Registered: 2008-03-27

Posts: 46

Re: Foil

ummm...okkkkkk....

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In this world of cheerios, be a fruitloop! ♥