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

Mar 17, 2018

$3 a \left({a}^{2} - 9 {b}^{2}\right)$

Explanation:

$3 {a}^{3} - 27 a {b}^{2}$

Since both numbers ($3$ and $- 27$) can be factored by $3$, let's take the $3$ out:
$3 \left({a}^{3} - 9 a {b}^{2}\right)$

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.
$3 a \left({a}^{2} - 9 {b}^{2}\right)$

After that, there is nothing else you can simplify. So, here's your answer:
$3 a \left({a}^{2} - 9 {b}^{2}\right)$

Hope this helps!! :)

Mar 17, 2018

3a  (a + 3b)( a - 3b)

Explanation:

Factor   3 a^3−27 a b^2

1) Factor out $3 a$ from each term

3a (a^2 - 9  b^2)

2) Factor the Difference of Two Squares

3a  (a + 3b)( a - 3b)