How do you factor $a^3 - (a-4)^3$ ?

Question

1532 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-15T15:00:17

$4(3a^2-12a+16)$

This is a difference of cubes, which factors into:

$x^3-y^3=(x-y)(x^2+xy+y^2)$

Here, we have $x=a$ and $y=(a-4)$ , which gives us a factorization of

$a^3-(a-4)^3$

$=(a-(a-4))(a^2+a(a-4)+(a-4)^2)$

We can continue to simplify.

$=(a-a+4)(a^2+a^2-4a+a^2-8a+16)$

$=4(3a^2-12a+16)$

This cannot be factored further (without the help of complex numbers).

How do you factor a^3 - (a-4)^3a^3 - (a-4)^3?