Factor 64x^3-1

Problem

64*x3−1

Solution

1. Identify the expression as a difference of two cubes, which follows the form a3−b3

2. Determine the cube roots of each term to find a and b

3. Calculate a by taking the cube root of 64*x3 which results in a=4*x

4. Calculate b by taking the cube root of 1 which results in b=1

5. Apply the formula for the difference of cubes: a3−b3=(a−b)*(a2+a*b+b2)

6. Substitute the values of a and b into the formula.

7. Simplify the terms within the second factor: (4*x)2=16*x2 (4*x)*(1)=4*x and 1=1

Final Answer

64*x3−1=(4*x−1)*(16*x2+4*x+1)

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