Question

PLEASE HELP REALLY NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!
WILL GIVE MEDAL!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

Find the constant term of expansion of the binomial (6x+1/3x)^6?

Answer 2

@amistre64 please help

Answer 3

might need some clarification on the notation, and a definition on what a constant term of expansion refers to

Answer 4

\[\frac1{3x}\]
or
\[\frac13x\]

Answer 5

So what to do after that?

Answer 6

Generally if you have (x^p + x^q)^n then you make things easier by
taking one term outside the bracket:

x^(np)[1 + x(q-p)]^n

= x^(np)[1 + C(n,1)x^(q-p) + C(n,2)x^(2(q-p)) + C(n,3)x^(3(q-p)) +..

The constant term would be C(n, r) where np + r(q - p) = 0 if an
integer value of r satisfies this equation.

http://mathforum.org/library/drmath/view/56428.html

Answer 7

amisster we can't find the answer if it is \[{1x/3}\]

Answer 8

the answer is 4th term

Answer 9

I am sorry I don't understand at all. Can you please explain this to me in depth. This is extra credit so it is essential that I get it right or my grade in math will be a B-!

Answer 10

Any help is appreciated.

Answer 11

then (r+1) term of the expantion (a+b)^n is
c(n,r)a^(n-r)*b^r

Answer 12

\[(6x+\frac13x^{-1})^6\]

\[(6x)^{6}(1+\frac1{18}x^{-2})^6\]

Answer 13

@amistre64 I will give the medal to @tony115 because you can't get much more higher than 99, is that okay with you?

Answer 14

fine by me, as long as they can elucidate the solution :)

Answer 15

what is the solution?

Answer 16

please say that do you understand my recent comment

Answer 17

if we take and actually expand it out we get this:

46656 x^6
+1/(729 x^6)
+15552 x^4
+4/(27 x^4)
+2160 x^2
+20/(3 x^2)
+160

im wondering of the 160 is what the question is asking for

Answer 18

I am sorry i didnt understand that last post @tony115

Answer 19

yes that the value of 4th term

Answer 20

in the expantion of \[(a+b)^n\] (r+1)th term is obtained by
c(n,r)\[a^{n-r}*b^{r}\]

Answer 21

sorry,\[c(n,r)a^{n-r}*b^{r}\]

Answer 22

so its the x^0 term ... i was confused on what it was actually asking for :)

Answer 23

160 was the right answer, thanks guys or gals!!!!!!

Answer 24

rob, you interpreted the question a little off. a = x^-1

Answer 25

bye

Answer 26

one more question

Answer 27

Expand (2x - 1)^5.