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- Nov 8th 2010, 12:26 AM #1

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## set f= x y z

set f = f(x,y,z) = (x^2 - y + 2z^3)^3

determine the coeffecients wwith which the following terms appear in F by using the multinomial theorem:

1) x^2 y^2

2) y^3

3) x^2 y z^3

4) y z^6

5) x y z

expres the following statements using quantifiers and usual mathematical symbols

1) the set of integers has no largest element

2) the differencee of two real numbers is a real number

- Nov 8th 2010, 02:31 AM #2

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- Nov 8th 2010, 03:02 AM #3

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i realised you got to find the coefficients, in the first one i can see x^2 but i cant see any y^2, but maybe it has to do with the ^3 outside of the bracket. the point i am stuck on is the multinomial theorem.

i have been researching a lot of websites and i dont understand the way they explain it, i can only find general rules which i dont get how to apply.

i think the answers has something in general to do with expanding the bracker. here is what i tried to prove i am not just being lazy

i went with: expanding it

x^6 + y^3 + 2z^9

and then take out

(X^4 + y + 2z^9) leaves x^2y^2 so the coefficient is (X^4 + y + 2z^9)?

- Nov 8th 2010, 03:09 AM #4

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- Nov 8th 2010, 08:43 AM #5

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- Nov 8th 2010, 09:58 AM #6

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youre awesome but what i dont get is how to use the multinomial when there are powers and numbers inside the bracket, i can do (x + y + z)^3 but i dont know what to do with powers inside, also i dont know what it means by terms, i know the nCr from the binomial and i know its about using factorial so that they add up to the n power (which is 3 in my question) but i dont know how to use it

also i dont get what you mean for i do 1 you do 2 what is the upiside down A ???

- Nov 8th 2010, 10:02 AM #7

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- Nov 8th 2010, 10:08 AM #8

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- Nov 8th 2010, 10:09 AM #9

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- Nov 8th 2010, 10:18 AM #10

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- Nov 8th 2010, 10:52 AM #11

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- Nov 8th 2010, 11:02 AM #12

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- Nov 8th 2010, 01:10 PM #13
Why not go to this website?

Type in. Click the equals sign at the extreme right of the input box. See what you get.**Expand (x^2-y+2z^3)^3**

- Nov 8th 2010, 01:42 PM #14

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- Nov 8th 2010, 01:57 PM #15