Para conocer la lógica de esto, vea cómo se ven las expansiones en Wolfram alpha (por ejemplo expand (xa)(xb)(xc)(xd)(xe) ).

 import java.util.ArrayList; import java.util.Arrays; import java.util.List; public class Main { public static void main(String[] args) { // (x-5)(x-4)(x-3)(x-2)(x-7) int[] xs = { 5, 4, 3, 2, 7 }; List<Integer> coefficients = new ArrayList<>(); boolean positive = true; for (int i = 0; i < xs.length + 1; ++i) { int coefficient = 0; if (i > 0) { List<int[]> combos = combos(xs, i); for (int[] nums : combos) { int product = 1; for (int num : nums) { product *= num; } coefficient += product; } } else { coefficient = 1; } coefficients.add(coefficient * (positive ? 1 : -1)); positive = !positive; } for (int i = 0; i < coefficients.size(); ++i) { int coefficient = coefficients.get(i); int exponenent = (coefficients.size() - i - 1); System.out.print(coefficient + "*x^" + exponenent + (exponenent == 0 ? "" : " + ")); } } // Combinations of xs size k private static List<int[]> combos(int[] xs, int k) { List<int[]> result = new ArrayList<>(); for (ArrayList<Integer> comboIdxs : combine(xs.length, k)) { int[] combo = new int[comboIdxs.size()]; for (int i = 0; i < comboIdxs.size(); ++i) { combo[i] = xs[comboIdxs.get(i)]; } result.add(combo); } return result; } // Thanks http://www.programcreek.com/2014/03/leetcode-combinations-java/ public static ArrayList<ArrayList<Integer>> combine(int n, int k) { ArrayList<ArrayList<Integer>> result = new ArrayList<ArrayList<Integer>>(); if (n <= 0 || n < k) return result; ArrayList<Integer> item = new ArrayList<Integer>(); dfs(n, k, 0, item, result); // because it need to begin from 1 return result; } private static void dfs(int n, int k, int start, ArrayList<Integer> item, ArrayList<ArrayList<Integer>> res) { if (item.size() == k) { res.add(new ArrayList<Integer>(item)); return; } for (int i = start; i < n; i++) { item.add(i); dfs(n, k, i + 1, item, res); item.remove(item.size() - 1); } } }