# How do I write the deterministic rate equation for bimolecular reaction with similar particles?

I was wondering how to write down the deterministic rate equation for a bimolecular reaction with similar particles.

e.g.

$$\ce{A ->[k_+] 2B}$$

and

$$\ce{2B ->[k_-] A}$$

Now the rate equations for the above reactions are:

$$\mathrm{\frac{\delta A}{\delta t}= - k_{+} A + k_{-} B^2}$$

$$\mathrm{\frac{\delta B}{\delta t}= 2 k_{+} A - 2 k_{-} B^2}$$

Now I have included a factor of 2 in the second equation to conserve $\mathrm{A + \frac{B}{2}}$.

But I don't understand the reasoning for this factor of 2 in the second equation.

$\frac{dB}{dt} = -2\frac{dA}{dt}$