Evaluate the binomial theorem!

Question

Your mission, even if you don't accept it, is to input three numbers from STDIN or file:

5 0.5 6

What you must do is evaluate this:

(5a + 0.5b)^6

This basically means that the first two numbers are the coefficients of a and b and the third is the exponent in a binomial expansion.

Rules:

The first two numbers are either integers or simple terminating fractions.
The third number is a positive integer.
Do not use any inbuilt binomial functions from libs. (thanks to comments)
The shortest code wins!

Go on, do it.

The interesting part of this has already been done as Generate Pascal's triangle — Peter Taylor
– Peter Taylor, Commented May 16, 2013 at 18:55
@PeterTaylor: not necessarily, for example the APL-like languages have binomials built in (as ! at least in APL and J). Indeed, the winner of that question used J's !. It would certainly have been longer if he had to hand-code it, and assuming that this question does not allow their use. — marinus
– marinus, Commented May 16, 2013 at 21:48
@GigaWatt: I'm assuming shortest code wins, since it's tagged as code-golf. — flornquake
– flornquake, Commented May 16, 2013 at 23:43

Dr. belisarius · Accepted Answer · 2013-05-17 13:41:38Z

Mathematica 36

InputForm@Expand[(#1 a + #2 b )^#3] &

Usage

InputForm@Expand[(#1 a + #2 b )^#3] &[5, .5, 6]

Result:

15625*a^6 +9375.*a^5*b +2343.75*a^4*b^2 +312.5*a^3*b^3 +23.4375*a^2*b^4 + 0.9375*a*b^5 + 0.015625*b^6

Ivan · Accepted Answer · 2013-05-16 22:20:25Z

F# 153 chars 156 bytes

let a,b,n=1.,2.,3 let rec C k=if k=0 then 1 else (n-k+1)*C(k-1)/k List.iter(fun i->printf"%+ga^%ib^%i"(pown a (n-i)*pown b i*float(C i)) (n-i) i)[0..n]

Jonathan Frech · Accepted Answer · 2017-11-05 23:57:25Z

Python 2, 144 bytes

a,b,n=input();f=lambda n:-~(n and~-n*f(~-n)) for k in range(-~n):print"+ "[0**k]+"%d*(%d*a^%d)*(%d*b^%d)"%(f(n)/f(k)/f(n-k),a**(n-k),n-k,b**k,k)

Try it online!

Community · Accepted Answer · 2020-06-17 09:04:33Z

C (C99), 223 chars

#include <stdio.h> #include <math.h> int f(int n,int k){ return k==0?1:(n*f(n-1,k-1))/k; } int main(void){ float a,b;int n; scanf("%f%f%d",&a,&b,&n); for(int k=0;k<=n;k++) printf("%d*(%fa)^%d*(%fb)^%d+",f(n,k),a,n-k,b,k); puts("0"); }

Input:

1 1 2

Output:

1*(1.000000a)^2*(1.000000b)^0+2*(1.000000a)^1*(1.000000b)^1+1*(1.000000a)^0*(1.000000b)^2+0

Do you have check if k==0? I think a simple k would do the same. — Johannes Kuhn
– Johannes Kuhn, Commented May 16, 2013 at 18:24

Stack Exchange Network

Evaluate the binomial theorem!

4 Answers 4

Mathematica 36

Python 2, 144 bytes

C (C99), 223 chars

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Evaluate the binomial theorem!

4 Answers 4

Mathematica 36

Python 2, 144 bytes

C (C99), 223 chars

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