Java Program to Compute a8-b8 where Value of a and b are Given

Java Program to Compute a8-b8 where Value of a and b are Given

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In the previous article we have discussed Java Program to Compute a5-b5 where Value of a and b are Given

In this program we are going to see how to compute a8-b8   where value of a and b are given by using Java programming language.

Java Program to Compute a8-b8 where Value of a and b are Given

The formula of a8-b8 is given below.

a8-b8  = (a4 + b4)(a2 + b2)(a + b)(a – b)

Now we will convert this into a valid Java expression.

Let x= a8-b8   

=  (a4 + b4)(a2 + b2)(a + b)(a – b)

=(a6 + a4b2 + a2b4 + b6)(a2 – ab + ab – b2)

=(a6 + a4b2 + a2b4 + b6)(a2 – b2)

=a8 + a6b2 + a4b4 +a2b6 – a6b2 – a4b4 – a2b6 – b8

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

Example:

Suppose a=4 and b=2, then

a8-b8
= (a*a*a*a*a*a*a*a)+(a*a*a*a*a*a*b*b)+(a*a*a*a*b*b*b*b)+(a*a*b*b*b*b*b*b)-(a*a*a*a*a*a*b*b)-(a*a*a*a*b*b*b*b)-(a*a*b*b*b*b*b*b)-(b*b*b*b*b*b*b*b)
= (4*4*4*4*4*4*4*4)+(4*4*4*4*4*4*4*2*2)+( 4*4*4*4 *2*2*2*2)+(4*4*2*2*2*2*2*2)-(4*4*4*4*4*4*2*2)-(4*4*4*4 *2*2*2*2)-(4*4*2*2*2*2*2*2)-(2*2*2*2*2*2*2*2)
= 65280

Now let’s see different ways to compute a8-b8   

Method-1: Java Program to Compute a8-b8 where Value of a and b are Given By Using Static Input Value

Approach:

  • Declare and initialize two integer variables say a and b.
  • By using the formula compute a8-b8  .
  • Print the result.

Program:

class Main
{
    public static void main(String[] args)
    {
        //declare the first integer variable with an integer value
        int a= 4;
        System.out.println("a= " +a);
        //declare the second integer variable with an integer value
        int b= 2;
        System.out.println("b= "+b);
        //declare another integer variable and assigned the formulated value to it.
        int c=(a*a*a*a*a*a*a*a)+(a*a*a*a*a*a*b*b)+(a*a*a*a*b*b*b*b)+(a*a*b*b*b*b*b*b)-(a*a*a*a*a*a*b*b)-(a*a*a*a*b*b*b*b)-(a*a*b*b*b*b*b*b)-(b*b*b*b*b*b*b*b);
        System.out.println("(a8 - b8)= "+c);
    }
}

Output:

a= 4
b= 2
(a8 - b8)= 65280

Method-2: Java Program to Compute a8-b8 where Value of a and b are Given By Using pow() Function

Approach:

  • Declare two integer variables say a and b.
  • Take the value of a and b as user input by using Scanner class.
  • Then By using the formula compute a8-b8  .
  • Here we have used inbuilt pow() function to compute the result.
  • 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();
        //declare another integer variable and assigned the formulated value to it.
        double  c= (Math.pow(a,8)) +( Math.pow( a,6)* Math.pow( b,2) )+ (Math.pow( a,4)* Math.pow( b,4) )+( Math.pow( a,2)* Math.pow( b,6))-( Math.pow( a,6)* Math.pow( b,2))-(Math.pow( a,4)* Math.pow( b,4))-(Math.pow( a,2)* Math.pow( b,6))- (Math.pow(b,8));
        System.out.println("a8 – b8= "+(int)c);
    }
}

Output:

a= 4
b= 5
a8 – b8= -325089

Method-3: Java Program to Compute a8-b8 where Value of a and b are Given By Using User Defined Method

Approach:

  • Declare two integer variables say a and b.
  • Take the value of a and b as user input by using Scanner class.
  • Then call a user defined method say computeValue() and pass a and b as parameter.
  • Then inside method by using the formula compute a8-b8  .
  • 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();
        //call the function
        computeValue(a,b);
    }
    //define the method
    public static void computeValue(int a, int b)
    {
        //declare another integer variable and assigned the formulated value to it.
        int c=(a*a*a*a*a*a*a*a)+(a*a*a*a*a*a*b*b)+(a*a*a*a*b*b*b*b)+(a*a*b*b*b*b*b*b)-(a*a*a*a*a*a*b*b)-(a*a*a*a*b*b*b*b)-(a*a*b*b*b*b*b*b)-(b*b*b*b*b*b*b*b);
        System.out.println("(a8 - b8)= "+c);
    }
}

Output:

a= 8
b= 10
(a8 - b8)= -83222784

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