Question

How do you factor `125a^3-c^3`?

Answer 1

`125a^3-c^3=(5a-c)*(25a^2+5ac+c^2)`

Explanation:

`125a^3-c^3=5^3a^3-c^3=(5a)^3-c^3`

Using the difference of two cubes rule:

`(b^3-d^3)=(b-d)(b^2+bd+d^2)`

with:

`b=5a`
`d=c`

`125a^3-c^3=(5a-c)(5^2a^2+5ac+c^2)=`
`=(5a-c)*(25a^2+5ac+c^2)`