Simplify (x-3)(x^2+3x+9)

Problem

(x−3)*(x^2+3*x+9)

Solution

1. Identify the structure of the expression as a product of a binomial and a trinomial.

2. Distribute the first term x to every term in the trinomial.

x*(x^2+3*x+9)=x^3+3*x^2+9*x

3. Distribute the second term −3 to every term in the trinomial.

−3*(x^2+3*x+9)=−3*x^2−9*x−27

4. Combine the results of the distribution.

x^3+3*x^2+9*x−3*x^2−9*x−27

5. Simplify by canceling out the like terms 3*x^2 and −3*x^2 as well as 9*x and −9*x

x^3−27

6. Recognize that this follows the difference of cubes formula where (a−b)*(a^2+a*b+b^2)=a^3−b^3

Final Answer

(x−3)*(x^2+3*x+9)=x^3−27

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