Factor x^2+100

Problem

x2+100

Solution

1. Identify the expression as a sum of two squares, which follows the form a2+b2

2. Recognize that a sum of squares cannot be factored using real numbers, but it can be factored using the imaginary unit i where i2=−1

3. Rewrite the expression as a difference of squares by changing the sign and incorporating i2 x2−(−100) which is x2−(10*i)2

4. Apply the formula for the difference of squares, a2−b2=(a−b)*(a+b) where a=x and b=10*i

Final Answer

x2+100=(x+10*i)*(x−10*i)

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