Factor 125x^3-1

Problem

125*x3−1

Solution

1. Identify the expression as a difference of two cubes, which follows the form a3−b3

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

3. Calculate a=√(3,125*x3)=5*x

4. Calculate b=√(3,1)=1

5. Apply the formula for the difference of cubes: a3−b3=(a−b)*(a2+a*b+b2)

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

7. Simplify the terms within the second factor: (5*x)2=25*x2 (5*x)*(1)=5*x and 1=1

Final Answer

125*x3−1=(5*x−1)*(25*x2+5*x+1)

Want more problems? Check here!