How do you factor $27a^3-8$ ?

Question

5256 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-07T18:02:47

$27a^3-8=color(red)((3a-2)(9a^2+6a+4))$

We have a difference of cubes:

$27a^3-8$

$=(3a)^3-2^3$

To factor a difference of cubes, use the formula:

$a^3-b^3=(a-b)(a^2+ab+b^2)$

$(3a)^3-2^3=color(red)((3a-2)(9a^2+6a+4))$

This cannot be factored any further using rational numbers, so this is the fully factored form.

How do you factor 27a^3-827a^3-8?