The math help thread

studying for physics exam, I stumple upon this equation on the textbook that doesn't make sense:

first it says:

m1(v1i-v1f)=m2(v2f-v2i)

then it says:

m1(v1i^2-v1f^2)=m2(v2f^2-v2i^2)

I don't get how they come up with the 2nd equation...

Formula #1 looks like conservation of momentum to me, while #2 looks like conservation of energy.
#1 = loss of momentum from 1st body is gained by 2nd body.
#2 = loss of energy (kinetic) from 1st body is gained by 2nd body.