Factor 2x^3-54

Problem

2*x3−54

Solution

1. Factor out the greatest common factor by identifying that both terms are divisible by 2

2*(x3−27)

2. Identify the difference of cubes pattern, noting that x3 is a perfect cube and 27 is 3

2*(x3−3)

3. Apply the difference of cubes formula, which states a3−b3=(a−b)*(a2+a*b+b2) where a=x and b=3

2*(x−3)*(x2+3*x+3)

4. Simplify the expression by calculating the square of 3

2*(x−3)*(x2+3*x+9)

Final Answer

2*x3−54=2*(x−3)*(x2+3*x+9)

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