def dup_mul_term(f, c, i, K):
    """
    Multiply ``f`` by ``c*x**i`` in ``K[x]``.

    Examples
    ========

    >>> R, x = ring("x", ZZ)

    >>> R.dmp_mul_term(x**2 - 1, ZZ(3), 2)
    3*x**4 - 3*x**2

    """
    if not c or not f:
        return []
    else:
        return [cf * c for cf in f] + [K.zero]*i