Factor x^2+81

Problem

x2+81

Solution

1. Identify the type of expression. This is a sum of squares in the form a2+b2 where a=x and b=9

2. Apply the complex factorization rule. A sum of squares cannot be factored using real numbers, but it can be factored over the complex numbers using the identity a2+b2=(a+b*i)*(a−b*i)

3. Substitute the values a=x and b=9 into the identity.

4. Simplify the resulting factors to obtain the final complex factorization.

Final Answer

x2+81=(x+9*i)*(x−9*i)

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