Question

How do you factor `8x^3y^6-125`?

Answer 1

`(2xy^2-5)(2x^2y^4+10xy^2+25)`

Explanation:

This is a difference of cubes, which takes the general form:

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

Recognize that `8x^3y^6=(2xy^2)^3` and that `125=5^3`.

`(2xy^2)^3-5^3=(2xy^2-5)((2xy^2)^2+2xy^2(5)+5^2)`

`=(2xy^2-5)(2x^2y^4+10xy^2+25)`