We recognize that $y^3$ is a perfect cube and $1000=10^3\text{,}$ so we can use Fact 7.5.15 to factor the binomial. Note that since we have a sum of cubes, the binomial factor from the formula will add two terms, and the middle term from the trinomial will be $-AB\text{.}$ $$\begin{aligned} y^3+1000\amp=(A+B)\left(A^2-AB+B^2\right)\\ \amp=(y+10)\left(y^2-(y)(10)+10^2\right)\\ \amp=(y+10)\left(y^2-10y+100\right) \end{aligned}$$