Math Help - set f= x y z

1. 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

2. Originally Posted by mathcore
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

This looks a lot like homework: what have you done, where are you stuck?

Tonio

3. 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)?

4. ive even tried tutorvista and it doesnt help me

5. Originally Posted by mathcore
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

Well, use the multinomial theorem! $(x^2-y+2z^3)^3=\displaystyle{\sum\limits_{k_1+k_2+k_3=3 }\binom{3}{k_1,k_2,k_3}(x^2)^{k_1}(-y)^{k_2}(2z^3)^{k_3}}$ .

Soy, what's the coefficient of $x^2y^2$ ? We'll get this when $k_1=1\,,\,k_2=2\Longrightarrow k_3=0$ , so the coefficient is

$\binom{3}{1,2,0}=\displaystyle{\frac{3!}{1!2!0!}}= 3$ , etc.

As for the other two questions: I do (1), you do (2):

$\forall x\in\mathbb{Z}\,\,\exists y\in\mathbb{Z}\,\,(y>x)$

Tonio

6. 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 ???

7. also the y is negative how do u deal with that

8. Originally Posted by mathcore
also the y is negative how do u deal with that

Who cares? If the power of y is odd the negative sign remains, and if the power of y is even it disappears...this is high school stuff!

Tonio

9. Originally Posted by mathcore
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 ???

Well, it is now obvious you're out of your depth: how come you try to answer a question asking you to use quantifiers and you ask the above?!?

Tonio

10. hello

there is no notes or book

i want to know, will the coefficients be always 3 or 6 since its 3!/2!1! or 3!/1s or 0s factorial, or will some be negative

what about the y^3 question, will this one be negative? the coefficient?

11. ok heres another thing i dont get:

number 5, it is asking for the coeff of XYZ, but the powers INSIDE the bracket are already higher than those
how do you deal with that?

12. ") the differencee of two real numbers is a real number"

ok would you say that xER and yER so X-Y = zER, is that how you do it?

13. Why not go to this website?

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

15. The term containing $y^1z^6$ is gotten by $\frac{3!}{k!\cdot j!}(-y)^k(2z^3)^j$ so that means $k=1~\&~j=2$.
$2^2=4~\&~4\cdot 3=12$