Binary Entropy Function (properties)

Question

I'm not a mathematician and I'm trying to understand the properties of the binary entropy function. In particular, I would like to ask you, if the distributive law can be applied to the following expression: $(x_i - y_i) H(\frac{1}{2^{i-1}}) \quad s.t. \quad x_i H(\frac{1}{2^{i-1}}) - y_i H(\frac{1}{2^{i-1}})$, without any violation of the $H$'s properties? Thank you in advance!