Factor 8x^3+64

Problem

8*x^3+64

Solution

1. Identify the common factor in both terms. Both 8*x^3 and 64 are divisible by 8

2. Factor out the greatest common factor 8 from the expression.

8*(x^3+8)

3. Recognize that the expression inside the parentheses, x^3+8 is a sum of two cubes because 8=2^3

8*(x^3+2^3)

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

8*(x+2)*(x^2−2*x+2^2)

5. Simplify the constant term inside the second set of parentheses.

8*(x+2)*(x^2−2*x+4)

Final Answer

8*x^3+64=8*(x+2)*(x^2−2*x+4)

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