Energy-Momentum Relation:
E2 = (m0c2)2 + (pc)2
Substitute mc2 for E (energy-mass equivilence)
Substitute mv for p (relation between mass, velocity, and momentum)
it should look like this:
(mc2)2 = (m0c2)2 + (mvc)2
Subtract (mvc)2 over..
(mc2)2 - (mvc)2 = (m0c2)2
m2c4 -...