Starting with the momentum equation for a fluid element in ideal MHD (ignoring viscosity and gravity):

\rho \frac{d}{dt} \bold{u} + \rho (\bold{u} \cdot \bold{\nabla}) \bold{u} = - \bold{\nabla} P + \frac{1}{\mu}(\bold{j} \times \bold{B})

The 2nd term on the RHS is the Lorentz force (or more accurately force per unit volume). Since we don't follow charges or currents, we rewrite it as:

\bold{j}\times\bold{B}= (\bold{\nabla} \times \bold{B})\times \bold{B}

which using a vector identity is rewritten as:

(\bold{\nabla} \times \bold{B})\times \bold{B}=-\bold{\nabla}(\frac{B^2}{2 \mu}) + \frac{1}{\mu}(\bold{B}\cdot \bold{\nabla}) \bold{B}