Question

1. Write a JAVA method that expands a given binomial (ax by)", where integers a, b, n are user inputs. For example, if a 2, b--12, n- 4 are entered the method should print or return (2x 12y)44- 16x*4 - 384xA3y 3456x 2y 2 13824xy 3 + 20736y 4 Use the Pascal's triangle method using only one 1-dim array to calculate all binomial coefficients. Your main program should use an appropriate loop for repeated inputs.

Write a JAVA method that expands a given binomial (ax + by)n, where integers a, b, n are user inputs. For example, if a = 2, b = -12, n = 4 are entered the method should print or return

(2x - 12y)^4 = 16x^4 - 384x^3y + 3456x^2y^2 – 13824xy^3 + 20736y^4

Use the Pascal’s triangle method using only one 1-dim array to calculate all binomial coefficients.

Answer 1

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package abc;

import java.util.*;

public class Binomial {

//Get coefficients.

static ArrayList<Long> getCoefficients(int n,ArrayList<Long> list){

for(int i = 1;i<=n;i++) {

int C = 1;

if(i==n)

for(int j =1;j<=i;j++) {

list.add((long)C);

C = C*(i-j)/j;

}

}

return list;

}

static void BinomialExpansion(int a, int b, int n) {

//(ax+by)^n

ArrayList<Long> list = new ArrayList<Long>();

list = getCoefficients(n+1,list);//the list of coefficients.

System.out.println(list);

String res = "";

//print the series.

for(int i = 0;i<list.size();i++) {

//constant term.

long constant = list.get(i)*(long)(Math.pow(a,n-i))*(long)(Math.pow(b,i));

String term = constant+"x^"+(n-i)+"y^"+i;

if(constant>0)

term = "+"+term;

res +=term;

}

System.out.println(res);

}

public static void main(String[] args) {

// TODO Auto-generated method stub

Scanner scan = new Scanner(System.in);

int t = scan.nextInt();

for(int i =0;i<t;i++) {

int a = scan.nextInt();

int b = scan.nextInt();

int n = scan.nextInt();

BinomialExpansion(a,b,n);

}

scan.close();

}

}

//output