Question

How do you factor `8y^3-125`?

Answer 1

`8y^3 - 125 = (2y-5)(4y^2+10y+25)`

Explanation:

The difference of cubes identity can be written:

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

Use this with `a=2y` and `b=5` as follows:

`8y^3 - 125 = (2y)^3-5^3`

`color(white)(8y^3 - 125) = (2y-5)((2y)^2+(2y)(5)+5^2)`

`color(white)(8y^3 - 125) = (2y-5)(4y^2+10y+25)`