# Java Program to Compute a5+b5 where Value of a and b are Given

In the previous article we have discussed Java Program to Compute a4-b4 where Value of a and b are Given

In this program we are going to see how to compute a5+b5   where value of a and b are given by using Java programming language.

## Java Program to Compute a5+b5 where Value of a and b are Given

The formula of a5+b5 is given below.

a5+b5  =  (a + b)(a4 – a3b + a2b2 – ab3 + b4)

Now we will convert this into a valid Java expression.

Let x= a5+b5

=  (a + b)(a4 – a3b + a2b2 – ab3 + b4)

=  a5 – a4b+a3b2 – a2b3 + ab4 + a4b – a3b2 + a2b3 – ab4 + b5

= (a*a*a*a*a) – (a*a*a*a*b) + (a*a*a*b*b) – (a*a*b*b*b) + (a*b*b*b*b)+ (a*a*a*a*b)  – (a*a*a*b*b)  + (a*a*b*b*b)  – (a*b*b*b*b)+ (b*b*b*b*b)

Example:

Suppose a=2 and b=2, then

a5+b5
= (a*a*a*a*a) - (a*a*a*a*b) + (a*a*a*b*b) - (a*a*b*b*b) + (a*b*b*b*b)+ (a*a*a*a*b)  - (a*a*a*b*b)  + (a*a*b*b*b)  - (a*b*b*b*b)+ (b*b*b*b*b)
= (2*2*2*2*2)- (2*2*2*2*2) + (2*2*2*2*2)- (2*2*2*2*2)+ (2*2*2*2*2)+ (2*2*2*2*2)- (2*2*2*2*2)+ (2*2*2*2*2)- (2*2*2*2*2)+ (2*2*2*2*2)
= 64

Now let’s see different ways to compute a5+b5

### Method-1: Java Program to Compute a5+b5 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 a5+b5  .
• 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*b) + (a*a*a*b*b) - (a*a*b*b*b) + (a*b*b*b*b)+ (a*a*a*a*b)  - (a*a*a*b*b)  + (a*a*b*b*b)  - (a*b*b*b*b)+ (b*b*b*b*b);
System.out.println("a5 + b5= "+c);
}
}

Output:

a= 4
b= 2
a5 + b5= 1056

### Method-2: Java Program to Compute a5+b5 where Value of a and b are Given By Using User Input Value

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 a5+b5  .
• 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,5)) - (Math.pow(a,4)*b)+ (Math.pow(a,3)* Math.pow(b,2)) - (Math.pow(a,2)* Math.pow(b,3)) + (a* Math.pow(b,4))+ (Math.pow(a,4)*b)  - (Math.pow(a,3)* Math.pow(b,2))  +(Math.pow(a,2)* Math.pow(b,3))  - (a* Math.pow(b,4))+ (Math.pow(b,5));
//Typecasting the value of c to integer value
System.out.println("a5 + b5= "+(int)c);
}
}


Output:

a= 4
b= 5
a5 + b5= 4149

### Method-3: Java Program to Compute a5+b5 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 a5+b5  .
• 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*b) + (a*a*a*b*b) - (a*a*b*b*b) + (a*b*b*b*b)+ (a*a*a*a*b)  - (a*a*a*b*b)  + (a*a*b*b*b)  - (a*b*b*b*b)+ (b*b*b*b*b);
System.out.println("a5 + b5= "+c);
}
}

Output:

a= 8
b= 10
a5 + b5= 132768

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