Answer
$(t+10)(t^2-10t+100)$
Work Step by Step
The expressions $
t^3
$ and $
1000
$ are both perfect cubes (the cube root is exact). Hence, $
t^3+1000
$ is a $\text{
sum
}$ of $2$ cubes. Using the factoring of the sum or difference of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2)$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(t)^3+(10)^3
\\\\=
(t+10)[(t)^2-t(10)+(10)^2]
\\\\=
(t+10)(t^2-10t+100)
.\end{array}
