Answer
$x^{2}.1+x^{2}.x+x^{2}\frac{1}{2!}x^{2}+...+\frac{1}{n!}x^n+...$
Work Step by Step
We are given $f(x)=x^{2}e^{x}$
with $c=x^{2}$ for $r$ in $(-\infty,\infty)$
The Taylor series for $f(x)=x^{2}e^{x}$ is
$f(x)=x^{2}.1+x^{2}.x+x^{2}\frac{1}{2!}x^{2}+...+\frac{1}{n!}x^n+...$
