Simplify x^3-27

Problem

x^3−27

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 to find the value of b

27=3^3

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

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

(x−3)*(x^2+(x)*(3)+3^2)

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

x^2+3*x+9

Final Answer

x^3−27=(x−3)*(x^2+3*x+9)

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