How to create predicate dynamically

Hi i want to create a list based on the search string using predicate expressions.

I have a list of type products contains different names.

List<products> list1 = new List<products>();

        list1.Add(new products("sowmya"));
        list1.Add(new products("Jane"));
        list1.Add(new products("John"));
        list1.Add(new products("kumar"));
        list1.Add(new products("ramya"));
        listBox1.ItemsSource = list1;

Now i want to filter the content based on user input.User will enter n no of strings with '+' as separator. After receiving the strings i will pass them to predicate object like this

 private void textBox1_KeyDown(object sender, KeyEventArgs e)
    {
        List<products> list2 = new List<products>();
        Expression<Func<products, bool>> predicate = PredicateBuilder.True<products>();
        if (e.Key == Key.Enter)
        {
            string Searchstring = textBox1.Text.ToString().Trim();
            string[] separator = new string[] { "+" };
            string[] SearchItems=Searchstring.Split(separator,StringSplitOptions.None);
            foreach (string str in SearchItems)
            {
                string temp = str;
                predicate =p => p.Name.Contains(temp.ToLower());                   
            }

            list2 = list1.AsQueryable().Where(predicate).ToList();
            listBox1.ItemsSource = list2;
        }
    }

If i enter more than one string(sowmya+jane+john) its giving only the last string(john) result but i want a list of all matching strings

Please answer this question because i'm trying this but i couldn't get the result.

Please do some help thanks.