Factor 125x^3+216

Problem

125*x^3+216

Solution

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

2. Determine the cube root of the first term, 125*x^3 which is 5*x Thus, a=5*x

3. Determine the cube root of the second term, 216 which is 6 Thus, b=6

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

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

6. Simplify the terms within the second factor: (5*x)^2=25*x^2 (5*x)*(6)=30*x and 6^2=36

Final Answer

125*x^3+216=(5*x+6)*(25*x^2−30*x+36)

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