MHB Why is this Maclaurin series incorrect?

[tmt1]

I need to find the Maclaurin series for

$$f(x) = x^2e^x$$

I know

$$e^x = \sum_{n = 0}^{\infty} \frac{x^n}{n!}$$

So, why can't I do

$$x^2 e^x =x^2 \sum_{n = 0}^{\infty} \frac{x^n}{n!} = \sum_{n = 0}^{\infty} \frac{x^2 x^n}{n!} $$

 

[Ackbach]

You can! I'd say you could combine the exponents in your final result:
$$x^2e^x=\sum_{n=0}^{\infty}\frac{x^{n+2}}{n!}.$$
Now this is a Maclaurin series, not a Taylor series expanded at a point other than $0$, right?