## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$(t+10)(t^2-10t+100)$
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}