Simplify (x-2)(x^2+2x+4)

Problem

(x−2)*(x^2+2*x+4)

Solution

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

2. Distribute the first term of the binomial, x to every term in the trinomial.

x*(x^2+2*x+4)=x^3+2*x^2+4*x

3. Distribute the second term of the binomial, −2 to every term in the trinomial.

−2*(x^2+2*x+4)=−2*x^2−4*x−8

4. Combine the results of the distribution.

x^3+2*x^2+4*x−2*x^2−4*x−8

5. Simplify by combining like terms, noting that 2*x^2−2*x^2=0 and 4*x−4*x=0

x^3−8

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−2)*(x^2+2*x+4)=x^3−8

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