math part of a physics problem

please help?

please help

left side: leave 1/2mv^2 as is it. expand the (v/R)^2. Now you'll get v^2/R^2. Multiply 2/5mR^2 * v^2/R^2. The R^2 cancels out and now you're left with 2/5mv^2. Multiply 2/5mv^2 by 1/2. You'll get 2/10mv^2 which can be simplified to 1/5mv^2. Add 1/5mv^2 with 1/2mv^2 and you'll get 7/10mv^2. Add that to the mgh and you get

7/10mv^2 + mgh

Right side: Do the exact same thing I described in the first part. The only difference is that v becomes v0.

>>161192
cancellation of R^2/R^2
then sum the fractions

>>161203
>>161206
anons you are gentlemen and scholars