Question

Identify whether the problem is "Sum of Two Cubes" or "Difference of Cubes". Then, factor the problem.x^3 - 8

Answer 1

We have in this case the difference of Perfect Cubes since we have:

`x^3-8=x^3-2^3`

We know that this case can be factored as follows:

`a^3-b^3=(a-b)\cdot(a^2+ab+b^2)`

If we have that:

a = x

b = 2

Then, we have:

`(x-2)\cdot(x^2_{}+2x+2^2)=(x-2)\cdot(x^2+2x+4)`

Therefore, the factored form of the perfect cube (for difference) is: