Factor x^3-216

Problem

x^3−216

Solution

1. Identify the expression as a difference of two cubes, which follows the form a^3−b^3

2. Rewrite the constant term as a cube by finding the cube root of 216 which is 6

x^3−6^3

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

4. Substitute a=x and b=6 into the formula.

(x−6)*(x^2+(x)*(6)+6^2)

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

(x−6)*(x^2+6*x+36)

Final Answer

x^3−216=(x−6)*(x^2+6*x+36)

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