How to deal with cross-terms in squared slashed covariant derivative in QED?

I am trying to compute the square of the slashed covariant derivative (the sum of the partial derivative and vector potential contracted with the gamma matrices) in terms of the square of the standard covariant derivative plus a term depending on the electromagnetic tensor and the commutator of the gamma matrices:

$$not D^2=D_μD^μ+ frac e 2 F_{μν}σ^{μν}$$ where $$not D = (partial_μ -ieA_μ)γ^μ$$ $$σ_{μν}=frac i2[γ^μ,γ^ν]$$ $$F_{munu} = partial_mu A_nu – partial_nu A_mu$$

However, I’m getting stuck with either $not A notpartial$ or $A_μ partial_nu σ^{μν}$ terms from the cross product which I’ve got not idea what to do with, since they’re clearly absent in the second term.