Question

Use the binomial formula to find the coefficient of the u^7m^3 term in the expansion of (u+2m)^10 .

Answer 1

Ever heard of Pascal's Triangle? That would be useful here

Answer 2

That thing has always confused me >.<

Answer 3

really? It's probably much easier than you think. You just start with 1....then 1 2 1, then
1 3 3 1, then 1 4 6 4 1....and just keep going until you get to the 10th row.

Answer 4

Hmm.. I kinda see where you're going with that but I'm not sure how I would use that to find the coefficient of u^7m^3 in (u+2m)^10 expanded.. haha sorry.. I'm dumb >.<

Answer 5

u^10+10u^9m+45u^8m^2+120u^7m^3.....

that's how

Answer 6

I painfully wrote out the Pascal's Triangle up to 10 levels deep...You can thank me later...

Answer 7

When you expand
\[(x+y)^{n}\]
using the binomial theorem, the kth term is:
\[\left(\begin{matrix}n \\ k-1\end{matrix}\right)x^{n-(k-1)}y^{k-1}\]
using this formula, the u^7m^3 term will be:
\[\left(\begin{matrix}10 \\ 3\end{matrix}\right)u^7(2m)^3\]
\[\left(\begin{matrix}10 \\ 3\end{matrix}\right) = \frac{10!}{3!(10-3)!} = \frac{10*9*8}{1*2*3} = 120\]
\[2^3 = 8\]
120*8 = 960
So the coefficient will be 960.

Answer 8

How come the co-efficient isn't 120?

Answer 9

because of the 2m. if it was just m it would be 120.

Answer 10

Yeah, you're right....forgot there are two variables

Answer 11

http://www.wolframalpha.com/input/?i=%28u%2B2m%29^10

Answer 12

But it's not 960 either...according to wolf

Answer 13

Sorry for delayed response but this site is acting up on me still. Thank you guys so very much for your help, I appreciate it! and thanks Hero for writing out Pascal's Triangle!

Answer 14

for some reason, they put the m first instead of u, i noticed that too lol. make sure you are looking at the u^7m^3 and not the m^7u^3 term.

Answer 15

You just wrote the same thing twice, lol

Answer 16

i switched the powers.

Answer 17

Oh, I see...

Answer 18

What do I know....I'm just an amateur

Answer 19

Way better at math than I Hero, that's for sure >.<

Answer 20

Yeah, but not good enough obviously