Factor x^3-8

Problem

x3−8

Solution

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

2. Rewrite the constant term as a cube to determine the values of a and b

x3−2

3. Apply the formula for the difference of cubes, which is a3−b3=(a−b)*(a2+a*b+b2)

4. Substitute a=x and b=2 into the formula.

(x−2)*(x2+(x)*(2)+2)

5. Simplify the terms inside the second set of parentheses.

(x−2)*(x2+2*x+4)

Final Answer

x3−8=(x−2)*(x2+2*x+4)

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