Question

How do you factor completely `3a^3 - 27ab^2`?

Answer 1

`3a ( a^2 - 9b^2)`

Explanation:

`3a^3 - 27ab^2`

Since both numbers (`3` and `-27`) can be factored by `3`, let's take the `3` out:
`3 ( a^3 - 9ab^2)`

Again, since both letters (`a^3` and `a`) have `a`'s in them, let's take the "`a`" out too! And remember, you can only take out `1` "`a`" because if you take out `2`, there aren't `2` `a`'s on the left group.
`3a ( a^2 - 9b^2)`

After that, there is nothing else you can simplify. So, here's your answer:
`3a ( a^2 - 9b^2)`

Hope this helps!! :)

Answer 2

`3a  (a + 3b)( a - 3b)`

Explanation:

Factor   `3 a^3−27 a b^2`

1) Factor out `3a` from each term

`3a (a^2 - 9  b^2)`

2) Factor the Difference of Two Squares

`3a  (a + 3b)( a - 3b)`