Hello I am asked to derive this formula by applying a binomial expansion to the expression for 'gamma factor' (that funny y shaped symbol). To make things clear I will denote gamma as 'y' and beta as 'b'

Now I know that yb = ((y-1)(y+1))^1/2 and have proved it by changing b into an expression for y to get the right side of the equation.

Now I am asked to use the binomial expansion on the expression for y to get this:

ymc^2 = mc^2 + 1/2mv^2

O_o

Which expression do I have to use? I read somewhere that objects at low speeds have y approaching to 1, how does this help me?