how do i prove that poisson becomes symmetric using the skewness formula as n becomes larger?

Question

I know that skewness should become 0, but i can't quite get how to show that with the equation.

I used the skewness formula and derived E[x^3] from E[x(x-1)(x-2)]. After that and plugging in the values to the SK formula, I ended up with (1-(λ^2))/(λ^(1/2)).