Factor 8x^3-64

Problem

8*x3−64

Solution

1. Identify the common factor in both terms. Both 8*x3 and 64 are divisible by 8

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

8*(x3−8)

3. Recognize the expression inside the parentheses as a difference of cubes, which follows the pattern a3−b3=(a−b)*(a2+a*b+b2)

4. Identify the values for a and b where a3=x3 and b3=8 This gives a=x and b=2

5. Apply the formula for the difference of cubes to factor x3−2

(x−2)*(x2+2*x+4)

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

8*(x−2)*(x2+2*x+4)

Final Answer

8*x3−64=8*(x−2)*(x2+2*x+4)

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