Simplify x^3-8

Problem

x^3−8

Solution

1. Identify the expression as a difference of two cubes, since x^3 is a cube and 8=2^3

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=2 into the formula.

4. Simplify the terms within the second factor by calculating 2^2=4

Final Answer

x^3−8=(x−2)*(x^2+2*x+4)

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