#### Answer

$(4t^{5}-1)^2$

#### Work Step by Step

Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
16t^{10}-8t^5+1
\end{array} has $ac=
16(1)=16
$ and $b=
-8
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-4,-4
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
16t^{10}-4t^5-4t^5+1
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(16t^{10}-4t^5)-(4t^5-1)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
4t^5(4t^{5}-1)-(4t^5-1)
.\end{array}
Factoring the $GCF=
(4t^{5}-1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(4t^{5}-1)(4t^5-1)
\\\\=
(4t^{5}-1)^2
.\end{array}