canyou help me factor x^3-x=

x(x^2 - 1)

(x)(x-1)(x+1)

Of course! To factor the expression x^3 - x, we can use a method called factoring by grouping. Here are the steps to factor it:

Step 1: Group the terms.
x^3 - x can be written as (x^3) + (-x).

Step 2: Factor out the greatest common factor from each group.
From the first group (x^3), we can factor out an 'x'. From the second group (-x), we can factor out a '-1'.

Step 3: Factor out the common factor.
By factoring out 'x' from the first group and '-1' from the second group, we get x(x^2 - 1).

Step 4: Further factor the remaining expression.
Now, we need to factor the expression (x^2 - 1). Notice that it is in the form of a difference of squares, meaning it can be factored as (x + 1)(x - 1).

Step 5: Final result.
Combining the results from step 3 and step 4, we have x(x + 1)(x - 1) as the factored form of x^3 - x.

Therefore, the factored form of x^3 - x is x(x + 1)(x - 1).