# What is difference between newton interpolation and lagrange interpolation?

I know that they both represent same polynomial and their formulas, but what is difference between them. If they are not different, then why do we study them separately?

Don't need detailed proof but general idea - 'what is going on?'

This is the same polynomial but you just find it in different ways. It's always better to have different ways because that way you have a lot more options. For example, if you want to have an easy formula for the remainder of the interpolation then it is much better to work with Newton's method. Another advantage is that if you found the interpolation polynomial in the points $x_0,x_1,...,x_n$ and then you want to add the point $x_{n+1}$ then using Newton's method you can use the polynomial in the points $x_0,...,x_n$ to easily find the polynomial for the points $x_0,...,x_{n+1}$. You don't have to find all the coefficients all over again.