Factor x^3-64

Problem

x3−64

Solution

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

2. Determine the values of a and b by taking the cube roots of each term.

3. Calculate a=√(3,x3)=x and b=√(3,64)=4

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

5. Substitute x for a and 4 for b into the formula.

6. Simplify the terms within the second factor to get x2+4*x+16

Final Answer

x3−64=(x−4)*(x2+4*x+16)

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