Answer:
Please see below
Step-by-step explanation:
Looks like the error is in the exponentiation of 2x
You have only raised x to the power of (6-k) not [tex](2x)^{6-k}[/tex] ie the entire term 2x should be exponentiated
For example, for k = 0 we should get
[tex]\binom{6}{0}\left(2x\right)^{6-0}\cdot2^{0}=\frac{6!}{\left(6-0\right)!0!}\left(2x\right)^{6-0}\cdot2^{0}=64x^{6}[/tex]
For k= 1, we should get
[tex]\binom{6}{1}\left(2x\right)^{6-1}\cdot2^{1}=\frac{6!}{\left(6-1\right)!1!}\left(2x\right)^{6-1}\cdot2^{1}=384x^{5}[/tex]
Use the same correction in the other terms
