Factor 125x^3-1

Problem

125*x^3−1

Solution

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

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

3. Calculate a=√(3,125*x^3)=5*x

4. Calculate b=√(3,1)=1

5. Apply the formula for the difference of cubes: a^3−b^3=(a−b)*(a^2+a*b+b^2)

6. Substitute a=5*x and b=1 into the formula.

7. Simplify the terms within the second factor: (5*x)^2=25*x^2 (5*x)*(1)=5*x and 1^2=1

Final Answer

125*x^3−1=(5*x−1)*(25*x^2+5*x+1)

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