A simple but useful identity is:
![\[\gamma^2-1=V^2\gamma^2\]](http://cmaclaurin.com/cosmos/wp-content/ql-cache/quicklatex.com-ae013018b0b0496debdb613db1074deb_l3.png "Rendered by QuickLaTeX.com")
This follows from the definition of the Lorentz factor γ in terms of a relative speed V between two frames:
![\[\gamma\equiv(1-V^2)^{-1/2}\]](http://cmaclaurin.com/cosmos/wp-content/ql-cache/quicklatex.com-15c3ad0110962165a700859ec1e52d4f_l3.png "Rendered by QuickLaTeX.com")
So
![\[\gamma^2-1=\frac{1}{1-V^2}-1=\frac{1-(1-V^2)}{1-V^2}=\frac{V^2}{1-V^2}=V^2\gamma^2\]](http://cmaclaurin.com/cosmos/wp-content/ql-cache/quicklatex.com-032b3f78f5feee909b9ed34bc625e3be_l3.png "Rendered by QuickLaTeX.com")
Alternatively raise both sides of the γ defining formula to the power of -2, obtaining 
, then multiply both sides by γ2 and rearrange.