Question

How do you factor `27x^3-125`?

Answer 1

`= (3x-5) (9x^"2" +15x+25)`

Explanation:

you can remember to factor difference between 2 cubes as this

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

so the answer to your question..

`27x^"3"−125` can be written as
`=3^"3"x^"3" - 5^"3"`
`= (3x-5) (9x^"2" +15x+25)`

FYI: an addition between 2 cubes can be written as this
`a^"3" + b^"3" = (a+b) (a^2 - ab + b^2)`
it's really easy when you remember those two equations by their patterns =)