# Java Program to Compute (a+b+c)(b+c-a)(c+a-b)(a+b-c) where Value of a, b, and c are Given

In the previous article we have discussed Java Program to Compute (b+c)(c+a)(a+b) where Value of a, b and c are Given

In this program we are going to see how to compute  (a+b+c)(b+c-a)(c+a-b)(a+b-c) where value of a, b, and c are given by using Java Programming language.

## Java Program to Compute (a+b+c)(b+c-a)(c+a-b)(a+b-c) where Value of a, b, and c are Given

The formula of (a+b+c)(b+c-a)(c+a-b)(a+b-c) is given below.

(a+b+c)(b+c-a)(c+a-b)(a+b-c) = 2a2b2 + 2b2c2 + 2c2a2 – a4 – b4 – c4

Now we will convert this into a valid Java expression.

Let x= (a+b+c)(b+c-a)(c+a-b)(a+b-c)

= 2a2b2 + 2b2c2 + 2c2a2 – a4 – b4 – c4

=  (2*a*a*b*b)+( 2*b*b*c*c)+( 2*c*c*a*a)-(a*a*a*a)-(b*b*b*b)-(c*c*c*c)

Or, (2*Math.pow(a,2)* Math.pow(b,2)) + (2*Math.pow(b,2)* Math.pow(c,2)) +   (2*Math.pow(c,2)* Math.pow(a,2)) – (Math.pow(a,4)) – (Math.pow(b,4)) – (Math.pow(c,4))

Example:

Suppose a=4, b=2 and c= 3, Then

(a+b+c)(b+c-a)(c+a-b)(a+b-c)
= (2*a*a*b*b)+( 2*b*b*c*c)+( 2*c*c*a*a)-(a*a*a*a)-(b*b*b*b)-(c*c*c*c)
= (2*4*4*2*2)+( 2*2*2*3*3)+( 2*3*3*4*4)-(4*4*4*4)-(2*2*2*2)-(3*3*3*3)
= 135

Now let’s see different ways to compute (a+b+c)(b+c-a)(c+a-b)(a+b-c)

### Method-1: Java Program to Compute (a+b+c)(b+c-a)(c+a-b)(a+b-c) where Value of a, b, and c are Given By Using Static Input Value

Approach:

• Declare and initialize two integer variables say a, b, and c.
• By using the formula compute (a+b+c)(b+c-a)(c+a-b)(a+b-c)
• Print the result.

Program:

class Main
{
public static void main(String[] args)
{
//declare the first integer variable with a integer value
int a= 4;
System.out.println("a= " +a);
//declare the second integer variable with a integer value
int b= 2;
System.out.println("b= "+b);
//declare the second integer variable with a integer value
int c= 3;
System.out.println("c= "+c);
//declare another integer variable and assigned the formulated value to it.
int d= (2*a*a*b*b)+( 2*b*b*c*c)+( 2*c*c*a*a)-(a*a*a*a)-(b*b*b*b)-(c*c*c*c);
System.out.println("(a+b+c)(b+c-a)(c+a-b)(a+b-c)= "+d);
}
}

Output:

a= 4
b= 2
c= 3
(a+b+c)(b+c-a)(c+a-b)(a+b-c)= 135

### Method-2: Java Program to Compute (a+b+c)(b+c-a)(c+a-b)(a+b-c) where Value of a, b, and c are Given y Using User Input Value and Pow()

Approach:

• Declare three integer variables say a, b, and c.
• Take the value of a, b, and c as user input by using Scanner class.
• Then By using the formula compute (a+b+c)(b+c-a)(c+a-b)(a+b-c)
• Print the result.

Program:

import java.lang.Math;
import java.util.Scanner;
class Main
{
public static void main(String[] args)
{
//create object of scanner class.
Scanner sc=new Scanner(System.in);
System.out.print("a= ");
//Take the first input from the user.
int a= sc.nextInt();
System.out.print("b= ");
//Take the second input from the user.
int b= sc.nextInt();
System.out.print("c= ");
//Take the first input from the user.
int c= sc.nextInt();
//declare another integer variable and assigned the formulated value to it.
double d= (2*Math.pow(a,2)* Math.pow(b,2)) + (2*Math.pow(b,2)* Math.pow(c,2)) +   (2*Math.pow(c,2)* Math.pow(a,2)) - (Math.pow(a,4)) - (Math.pow(b,4)) - (Math.pow(c,4));
System.out.println("(a+b+c)(b+c-a)(c+a-b)(a+b-c)= "+(int)d);
}
}

Output:

a= 34
b= 45
c= 56
(a+b+c)(b+c-a)(c+a-b)(a+b-c)= 9361575

### Method-3: Java Program to Compute (a+b+c)(b+c-a)(c+a-b)(a+b-c) where Value of a, b, and c are Given By Using User Defined Method

Approach:

• Declare two integer variables say a, b, and c
• Take the value of a, b, and c as user input by using Scanner class.
• Then call a user defined method say computeValue() and pass a, b, and c as parameter.
• Then inside method by using the formula compute (a+b+c)(b+c-a)(c+a-b)(a+b-c)
• Print the result.

Program:

import java.util.Scanner;
class Main
{
public static void main(String[] args)
{
//create object of scanner class.
Scanner sc=new Scanner(System.in);
System.out.print("a= ");
//Take the first input from the user.
int a= sc.nextInt();
System.out.print("b= ");
//Take the second input from the user.
int b= sc.nextInt();
System.out.print("c= ");
//Take the first input from the user.
int c= sc.nextInt();
//call the function
computeValue(a,b,c);
}

//define the method
public static void computeValue(int a, int b,int c)
{
//declare another integer variable and assigned the formulated value to it.
int d= (2*a*a*b*b)+( 2*b*b*c*c)+( 2*c*c*a*a)-(a*a*a*a)-(b*b*b*b)-(c*c*c*c);
System.out.println("(a+b+c)(b+c-a)(c+a-b)(a+b-c)= "+d);
}
}

Output:

a= 12
b= 34
c= 32
(a+b+c)(b+c-a)(c+a-b)(a+b-c)= 589680

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