Question

How do you factor `125e^3-27f^3`?

Answer 1

`(5e-3f)(25e^2+15ef+9f^2)`

Explanation:

`"this is a "color(blue)"difference of cubes"`

`•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)`

`125e^3=(5e)^3rArra=5e`

`27f^3=(3f)^3rArrb=3f`

`=(5e-3f)((5e)^2+5e*3f+(3f)^2)`

`=(5e-3f)(25e^2+15ef+9f^2)`

Answer 2

`(5e-3f)(25e^2+15ef+9f^2)`

Explanation:

What we have is a difference of cubes, which factors as follows:

`bar(ul|color(white)(2/2)(a^3-b^3)=(a-b)(a^2+ab+b^2)color(white)(2/2)|`

We have the following:

`125e^3-27f^3`, where `a=root3(125e^3)`, and `b=root3(27f^3)`.

Simplifying these, we get `a=5e` and `b=3f`. Let's plug these into our difference of cubes expression to get

`(5e-3f)(25e^2+15ef+9f^2)`

Hope this helps!