Find the coefficient of the constant term of the expression (2x+1/(4x^3 ))^8

In order to find the coefficient we need to know which term of the binomial expansion is constant. We know the expression to find the coefficient is (8Cn)(2^n)((1/4)^(8-n)), where n is the power we are rising each variable and the variables coefficients are risen to the same power as the variables. We know both terms have a variable so we want the value n for which the variables null each other. Hence, we are looking for the term when n-3*(8-n)=0 (the -3 term comes from it being a negative power), which we can rearrange to 4n -24=0, hence n=6.Having the value of n we put it in the binomial formula and obtain the result 112.