Factor 27x^3-125

Problem

27*x3−125

Solution

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

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

3. Calculate a by taking the cube root of 27*x3 which is 3*x

4. Calculate b by taking the cube root of 125 which is 5

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

6. Substitute a=3*x and b=5 into the formula.

7. Simplify the terms within the second factor: (3*x)2=9*x2 (3*x)*(5)=15*x and 5=25

Final Answer

27*x3−125=(3*x−5)*(9*x2+15*x+25)

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