Answer
$x^4+2x^2+1$
Work Step by Step
Using $(a\pm b)^2=a^2\pm2ab+b^2$ or the square of a binomial, the square of the given expression, $\left(
x^2+1
\right)^2,$ is
\begin{array}{l}\require{cancel}
(x^2)^2+2(x^2)(1)+(1)^2
\\\\=
x^4+2x^2+1
.\end{array}