Factor 2x^3+54

Problem

2*x^3+54

Solution

1. Factor out the greatest common factor, which is 2

2*(x^3+27)

2. Identify the expression inside the parentheses as a sum of two cubes, since 27=3^3

2*(x^3+3^3)

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

2*(x+3)*(x^2−(x)*(3)+3^2)

4. Simplify the terms inside the second set of parentheses.

2*(x+3)*(x^2−3*x+9)

Final Answer

2*x^3+54=2*(x+3)*(x^2−3*x+9)

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