For the logic of this, see what the expansions look like on Wolfram alpha (e.g. expand (x-a)(x-b)(x-c)(x-d)(x-e)).

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);
        }
    }
}