Functions

Let c, k \(\in\) R. If \(f(x) = (c + 1){x^2} + (1 - {c^2})x + 2k\) and \(f(x + y) = f(x) + f(y) - xy\), for all x, y \(\in\) R, then the value of \(|2(f(1) + f(2) + f(3) + \,\,......\,\, + \,\,f(20))|\) is equal to ____________.