Factor x^3-x

Problem

x^3−x

Solution

1. Identify the greatest common factor in both terms of the expression.

2. Factor out the common term x from the expression.

x*(x^2−1)

3. Recognize that the remaining term x^2−1 is a difference of squares, which follows the pattern a^2−b^2=(a−b)*(a+b)

4. Factor the difference of squares x^2−1 into (x−1)*(x+1)

x*(x−1)*(x+1)

Final Answer

x^3−x=x*(x−1)*(x+1)

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