Einstein summation convention in deriving Coulomb's law

Schwartz’s QFT equation (3.43) reads

$$ mathcal{L} = – frac{1}{4} (partial_mu A_nu – partial_nu A_mu)^2 – A_mu J_mu. tag{3.43}$$

Does the contraction of $mu$ on the last term carry over to the first term? In particular, is it the same as saying:

$$ mathcal{L} = – frac{1}{4} (partial_t A_nu + partial_x A_nu + partial_y A_nu + partial_z A_nu – partial_nu A_t – partial_nu A_x – partial_nu A_y – partial_nu A_z)^2 $$
$$- A_t J_t – A_x J_x – A_y J_y – A_z J_z~? $$