Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises - Page 34: 82

$1+1000y^{3}=(1+10y)(1-10y+100y^{2})$

$1+1000y^{3}$ This is a sum of cubes. The formula to factor an expression like this is $A^{3}+B^{3}=(A+B)(A^{2}-AB+B^{2})$ For this expression, $A^{3}=1$ and $B^{3}=1000y^{3}$ $1+1000y^{3}=(1+10y)(1-10y+100y^{2})$