Given the expression $E=(1+3x+8x^2)^{12}$ . I was trying to find the numerically greatest coefficient of any power of x in the above expression.
My try
I wrote the general coefficient as
$(10)! (3^p)(8^q)/{(p!)(q!)(10-p-q)!} $ However I am unable to maximise this expression. I was hoping for some hints or an alternate solution ?