How to prove (-x)³ = -(x³) for all real x

[Airaya]

Homework Statement

Prove for all xεR [(-x)³ = -(x³)]
(Hint you may use the fact that -x = (-1)*x, but other wise stick to axioms)
I wrote something along the lines of .
(-x)³ can be written as (-1)(x)(x)(x) and -(x)³ can be written as (-1)((x)(x)(x))
and these are both equivalent
But it doesn't feel like I'm proving anything.
Not sure how to really write this out so there is enough "proof"

 

[HallsofIvy]

I think the point you are missing is that (-x)³ "can be written as" (-x)(-x)(-x) and then you can show that is equal to -(x)(x)(x).