Factor 5x^3-135

Problem

5*x^3−135

Solution

1. Factor out the greatest common factor by identifying that both terms are divisible by 5

5*(x^3−27)

2. Identify the difference of cubes within the parentheses, noting that x^3 is a cube and 27 is 3^3

5*(x^3−3^3)

3. Apply the difference of cubes formula, which states a^3−b^3=(a−b)*(a^2+a*b+b^2) where a=x and b=3

5*(x−3)*(x^2+3*x+3^2)

4. Simplify the expression by calculating the square of 3

5*(x−3)*(x^2+3*x+9)

Final Answer

5*x^3−135=5*(x−3)*(x^2+3*x+9)

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