  We extend the Newton's method and show the extended Newton's method leads to
the binomial expansion of Newton's method that the convergences become the
quadratic and linearly. In case of the quadratic convergence, we give the
convergence comparison of the binomial expansion of Newton's method and
Newton's method. And we give convergence comparisons of the binomial expansion
of Newton's method and Newton's method using the curvature and convex-concave
of curve. Next we give examples of numerical calculations of the binomial
expansion of Newton's method.
