Do I have to standardize my new polynomial features? I have a vector X with n features previously standardized.

If I want to generate new polynomial features (let say adding square features), do I need to do another standardization on these new features after the computing ? 

Because knowing that my original features are already between 0 and 1, the new polynomial features will also be between 0 and 1. But the higher the degree is, the higher the "ratio" between the original one and the polynomial one will be.

Also,  would that be better to do the square computing on the values of the non standardized features, and then standardize these new features ?

By the way, when I say "standardization", I m thinking about substrat each value by the mean and divide it by the std.

Thanks in advance,

Regards.
It's better to do the square computing on the values of the non standardized features, and then standardize these new features. 

The point of standardizing features is to put features in a similar scale, e.g. 0-1. If you didn't standardize these new features after the computing, although your new features are between 0-1, your new features will be one or more magnitude smaller than your old features.