Factor 125x^3-64

Problem

125*x^3−64

Solution

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

2. Determine the cube roots of each term to find a and b

3. Calculate a by taking the cube root of 125*x^3

a=√(3,125*x^3)=5*x

4. Calculate b by taking the cube root of 64

b=√(3,64)=4

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

6. Substitute the values of a and b into the formula.

(5*x−4)*((5*x)^2+(5*x)*(4)+4^2)

7. Simplify the terms inside the second factor.

(5*x−4)*(25*x^2+20*x+16)

Final Answer

125*x^3−64=(5*x−4)*(25*x^2+20*x+16)

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