Factor 2x^3-16

Problem

2*x^3−16

Solution

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

2*(x^3−8)

2. Identify the expression inside the parentheses as a difference of cubes, since 8=2^3

2*(x^3−2^3)

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

2*(x−2)*(x^2+2*x+2^2)

4. Simplify the constant term in the quadratic factor.

2*(x−2)*(x^2+2*x+4)

Final Answer

2*x^3−16=2*(x−2)*(x^2+2*x+4)

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