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 sum of two cubes, using the form a^3+b^3 where a=x and b=2

x^3+2^3

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

(x+2)*(x^2−2*x+2^2)

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

(x+2)*(x^2−2*x+4)

5. Combine the common factor from the first step with the factored expression.

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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