Answer
$A=(x^4+16x^2+64)\text{ square units}$
Work Step by Step
Using $A=s^2$, the area of the square with side measurement equal to $
(x^2+8)
$ is
\begin{array}{l}\require{cancel}
A=(x^2+8)^2
.\end{array}
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression above is equivalent to
\begin{array}{l}\require{cancel}
A=(x^2)^2+2(x^2)(8)+(8)^2
\\\\
A=x^4+16x^2+64
\\\\
A=(x^4+16x^2+64)\text{ square units}
.\end{array}