Factor x^2+36

Problem

x2+36

Solution

1. Identify the expression as a sum of squares in the form a2+b2 where a=x and b=6

2. Apply the formula for factoring a sum of squares over the complex numbers, which is a2+b2=(a+b*i)*(a−b*i)

3. Substitute the values a=x and b=6 into the complex factoring formula.

4. Verify the result by expanding (x+6*i)*(x−6*i) to ensure it equals x2−(6*i)2=x2−(−36)=x2+36

Final Answer

x2+36=(x+6*i)*(x−6*i)

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