# Any quick tricks to multiplying by powers?

## Main Question or Discussion Point

Hey guys

Basically I want to evaluate ((1/3 +x/2 +x3/6))3

But instead of doing the long hand is there any way off doing this quickly? Basically I was wanting to find the coefficient of x3?

So ya any tricks because I seem to remember doing something like 3(1/3*1/2*1/6) +... can't remember..

Regards
Tam

phyzguy
What you want are called 'multinomial coefficients' - here's a link:
http://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients

For your problem, if you consider this of the form (a+b+c)^3, there are two ways to get x^3, you can have a^2*c, or you can have b^3. The coefficients of these will be :

Coef(a^2 c) = 3!/(2! 0! 1!) , and
Coef(b^3) = 3!(0! 3! 0!)

Hopefully from there you can work out the coefficient of x^3. If you do that, what do you get?

Thanks.. Okay we need:Ʃn!/p!q!r! For apbqcr

So does that give us the coeff of x3 = 3 + 1 = 4... doesn't seem right...

Any help would be great!?

Thanks

phyzguy
No, you need:

(1) c^3 + (3) a^2 c =

(1) (x/2)^3 + (3) (1/3)^2 (x^3/6) = (What) x^3

No, you need:

(1) c^3 + (3) a^2 c =

(1) (x/2)^3 + (3) (1/3)^2 (x^3/6) = (What) x^3
Okay using what you wrote I get 13/72. This is correct as I have checked with my answer.. However I am unsure of why you multiplied b3 by (1) and a2c by (3)?

Thanks for you help
Regards
Tam

phyzguy