database – wp search multiple search terms

i have this code

It works perfect if I search for 1 term but when I add 2 terms to search it fails

    function product_title_like_where ( $where, &$wp_query ) {
    global $wpdb;

    if ( $search_term = $wp_query->get( 'product_title_like' ) ) {
        $where .= ' AND ' . $wpdb->posts . '.post_title LIKE '%' . esc_sql( like_escape( $search_term ) ) . '%'';
    }

    return $where;
}

So, for example, if I'm looking for XX matches, but if I'm looking for XX X2, I can't find

thanks