Question

How do you factor `8000 + y^3`?

Answer 1

Use the sum of cubes identity to find:

`8000+y^3=(20+y)(400-20y+y^2)`

Explanation:

Both `8000 = 20^3` and `y^3` are perfect cubes.

Use the sum of cubes identity:

`a^3+b^3 = (a+b)(a^2-ab+b^2)`

with `a=20` and `b=y` as follows:

`8000+y^3`

`=20^3+y^3`

`=(20+y)(20^2-20y+y^2)`

`=(20+y)(400-20y+y^2)`