How to multiply polynomial given in divided differences representation by a number?

How to multiply polynomial p(x) given in Newton's divided-difference 
representation dd[N], xa[N] by a scalar: a*p(x)? I want to to find 
divided-difference representation dda[N], xaa[N] for a*p(x) polynomial.

In standard monomial representation p(x) = b[0] + b[1]*x +...+ b[n]*x^n
multiplying by scalar is simple a*p(x) = a*b[0] + ... + a*b[n]*x^n.
How to do the same in divided-difference representation?
 
-- 
Jakub Narebski
Poland