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 the expression inside the parentheses as a difference of cubes, which follows the pattern a^3−b^3=(a−b)*(a^2+a*b+b^2)

4. Identify the values for a and b where a^3=x^3 and b^3=8 This gives a=x and b=2

5. Apply the formula for the difference of cubes to factor x^3−2^3

(x−2)*(x^2+2*x+4)

6. Combine the greatest common factor with the factored binomial and trinomial.

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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