When we expand (2x+1/2)^6 what is the coeeficent of the term x^4?

We can use the Binomial Theorem here! (although you can also use the Pascal's Triangle method, I just prefer to use this)

 

(6!/(2!6-2)!)(2x)^4(1/2)^2 = 15*16x*1/4 = 60x^4

 

So therefore our coefficient is 60!

Hope this helps!