Factorising Problem Solutions: 32x^3(2x^2+1)+8x(2x^2+1)^2

[rudders93]

Homework Statement

It's a calculus problem. But I can get all that, it's just this final bit of factorising the answer that has me stumped. The answer I get is correct (as my calculator factorises it into the same answer as the book has), but I've been looking at it and I can't seem to figure out how to factorise it. So I was wondering if someone could please show the steps / techniques used to factorise this problem:

Homework Equations

Factorise $(32x^3(2x^2 + 1) + 8x(2x^2 + 1)^2)$

The Attempt at a Solution

I tried taking out 8x as the common factor to get to: $8x(4x^2(2x^2 + 1) + (2x^2 + 1)^2))$ but I still can't see any way to further simplify it.

The answer by the way (according to my calculator / book) is: $8 x (2 x^2+1) (6 x^2+1)$

Thanks!

 

[Mark44]

You can take out 8x(2x² + 1) from each term. What do you have left?

 

[rudders93]

Ah. Gotcha. Thanks!

 

[Tevion]

8 x (2 x^2+1) (6 x^2+1)