Chain Rule - Book Example

I am having trouble understanding a portion of the textbook example. It's seems to be mostly with the simplifing of the answer.

Find dy/dx if y = u^3 - 3u^2 + 1 and u = x^2 + 2

dy/du = 3u^2 - 6u and du/dx = 2x

it follows that dx/dy = (3u^2 - 6u)(2x). *I'm fine so far, keep going*

We are substituting x^2 + 2 for u in the expression for dy/dx giving

[3(x^2+2)^2 - 6(x^2+2)](2x)

*I understand everything above but the next step confuses me*

6x(x^2+2)[(x^2+2)-2]

I don't know what steps they took to arrive at that equation. Could you possible show me the 'longer' process?

It goes on to give:

6x(x^2+2)(x^2)=

6x^3(x^2+2)