Factor x^3-512

Problem

x^3−512

Solution

1. Identify the expression as a difference of two cubes. The number 512 can be written as 8^3

2. Apply the formula for the difference of cubes, which is a^3−b^3=(a−b)*(a^2+a*b+b^2)

3. Substitute a=x and b=8 into the formula.

4. Simplify the terms within the second factor by calculating 8^2 and x⋅8

Final Answer

x^3−512=(x−8)*(x^2+8*x+64)

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