ExpressionTerm.java

public class ExpressionTerm implements Comparable{
    double coefficient;
    double exponent;
    
    // getter and setter
    
    public int compareTo(ExpressionTerm term){
        if (this.exponent < term.exponent) return -1;
        if (this.exponent == term.exponent) return 0;
        if (this.exponent > term.exponent) return 1;
    }
    
    public ExpressionTerm add(ExpressionTerm term){
        // here we should also check if both terms have the same exponent
        // if not we should throw expcetions.
        ExpressionTerm result = new ExpressionTerm();
        result.coefficient = this.coefficient + term.coefficient;
        result.exponent = this.exponent;
        return result;
    }
}

PolynomialAddition.java

import java.util.Arrays;
public class PolynomialAddition{
    public ExpressionTerm[] sum(ExpressionTerm[] exp1, ExpressionTerm[] exp2){
        if(exp1 == null) return exp2;
        if(exp2 == null) return exp1;
        
        Arrays.sort(exp1);
        Arrays.sort(exp2);
        
        // if there are terms with the same exponents but not merged together
        // we could implement another function to merge them
        // exp1 = mergeTermsWithSameExponent(exp1);
        // exp2 = mergeTermsWithSameExponent(exp2);
        
        int len1 = exp1.length;
        int len2 = exp2.length;
        
        // merge the two expressions together into a new one
        int len = len1 > len2 ? len1 : len2;
        ExpressionTerm[] total = new ExpressionTerm[len];
        
        int i = 0;
        int j = 0;
        int k = 0;
        while(i < len1 && j < len2){
            total[k++] = exp1[i++].add(exp2[j++]);
        }
        
        if(i == len1){
            while(j < len2) total[k++] = exp2[j++];
        }else{
            while(i < len1) total[k++] = exp2[i++];
        }
        return total;
    } 
}