10 points help?

8x³ - 125

Showing the general form of factoring difference of two cubes is pretty much all the "show work" you need.

general form is:

a³ - b³ = (a - b)(a² + ab + b²)

So in your case, we can set:

a = 2x and b = 5

Then we get:

(2x)³ - 5³ = (2x - 5)((2x)² + 2x(5) + 5²)

Then simplify:

(2x)³ - 5³ = (2x - 5)(4x² + 10x + 25)

And that's as simplified as you'll get. Most people don't worry about factoring over irrationals and complex unless specifically told to. So that's your factored form.

Updated with Corrections:

Factor: Difference of Cubes
8x^3-125
a^3-b^3=(a-b)(a^2+ab+b^2)
so a = 2x since (2x)^3 = 8x^3
so b = 5 since (5)^3 = 125
===== answer if you only want real factoring
8x^3-125= (2x - 5)*(4x^2 +10x + 25)
Use quadratic formula for 4x^2 +10x + 25
x= (10 +/- sqrt ( 10^2 -4*4*25) ) / 8
since (10^2 -400) is negative all answer for x are imaginery
x = (-10 +/- sqrt (-300) ) / 8
x = -5/4 +/- 10*sqrt(-3)/ 8
x = -5/4 +/- 5/4*sqrt(3)*i
=== including imaginary factors
(2x -5)*( x + (5/4) + (5*sqrt(3)/4)*i )*(( x + (5/4) - (5*sqrt(3)/4)*i )

8x^3 - 125 - Is not a difference of cubes. The answer is: (2x - 5)(4x^2 + 10x + 25)

The second answer is correct.