Assume the following bi-molecular reaction is elementary as written with rate constant $k_\mathrm{f}$: $$\ce{A + A -> P}$$
This review, suggests to express the rate in terms of the production of product "P": \begin{align} \frac{\mathrm{d}[\ce{P}]}{\mathrm{d}t} &= k_\mathrm{f}[\ce{A}]^{2},& \text{where } \frac{\mathrm{d}[\ce{P}]}{\mathrm{d}t} &= \left(-\frac{1}{2}\right)\frac{\mathrm{d}[\ce{A}]}{\mathrm{d}t}, \end{align} which gives: $$\frac{\mathrm{d}[\ce{A}]}{\mathrm{d}t} = -2k_\mathrm{f}[\ce{A}]^{2}.\tag{1}$$
While this other review suggests that the rate be written in terms of the consumption of reactant "$\ce{A}$": $$\frac{\mathrm{d}[\ce{A}]}{\mathrm{d}t} = -k_\mathrm{f}[\ce{A}]^{2}.\tag{2}$$
Which is correct?