Factor x^3-1

Problem

x^3−1

Solution

1. Identify the expression as a difference of cubes, which follows the general form a^3−b^3

2. Determine the values of a and b by taking the cube roots of each term.

3. Substitute a=x and b=1 into the difference of cubes formula: a^3−b^3=(a−b)*(a^2+a*b+b^2)

4. Simplify the resulting terms within the parentheses.

Final Answer

x^3−1=(x−1)*(x^2+x+1)

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