Java Program to Compute a4+a2b2+b4 where Value of a and b are Given

In the previous article we have discussed Java Program to Compute a3-b3+c3+3abc where Value of a, b and c are Given

In this program we are going to see how to compute a⁴+a²b²+b⁴where value of a and b are given by using Java programming language.

Java Program to Compute a4+a2b2+b4 where Value of a and b are Given

The formula of a⁴+a²b²+b⁴ is given below

a⁴+a²b²+b⁴ = (a² + b² + ab)(a² + b² – ab)

Now we will convert this into a valid Java expression

Let x= a⁴+a²b²+b⁴

= (a²+ b² + ab)(a² + b² – ab)

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

Example:

Suppose a=2 and b=2, Then
a2+a2b2+b4
= ((a*a) + (b*b) – (a*b))*((a*a) + (b*b) – (a*b))
= ((2*2) + (2*2) – (2*2))*((2*2) + (2*2) – (2*2))

Now let’s see different ways to compute a⁴+a²b²+b⁴

By Using Static Input Value
By Using User Input Value and Pow() Function
By Using User Defined Method

Method-1: Java Program to Compute a4+a2b2+b4 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 a⁴+a²b²+b⁴
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) + (b*b) + (a*b))*((a*a) + (b*b) - (a*b));
        System.out.println("a4+a2b2+b4 = "+c);
    }
}

Output:

a= 4
b= 2
a4+a2b2+b4 = 336

Method-2: Java Program to Compute a4+a2b2+b4 where Value of a and b are Given By Using User Input Value and Pow() Function

Approach:

Declare two integer variables say a and b.
Prompt the user to enter the values to the corresponding variables by using Scanner class.
Then By using the formula compute a⁴+a²b²+b⁴
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,2)+Math.pow(b,2)+(a*b))*( Math.pow(a,2)+Math.pow(b,2)-(a*b));
        //Typecasting the value of c to integer value
        System.out.println("a4+a2b2+b4= "+(int)c);	
    }
}

Output:

a= 12
b= 11
a4+a2b2+b4= 52801

Method-3: Java Program to Compute a4+a2b2+b4 where Value of a and b are Given By Using User Defined Method

Approach:

Declare two integer variables say a and b.
Prompt the user to enter the values to the corresponding variables 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 a⁴+a²b²+b⁴^.
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) + (b*b) + (a*b))*((a*a) + (b*b) - (a*b));
        System.out.println("a4+a2b2+b4 = "+c);
    }
}

Output:

a= 4
b= 5
a4+a2b2+b4 = 1281

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