Factor x^2+25

Problem

x2+25

Solution

1. Identify the expression as a sum of squares in the form a2+b2 where a=x and b=5

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=5 into the complex factoring formula.

4. Verify the result by expanding (x+5*i)*(x−5*i)=x2−(5*i)2=x2−25*i2=x2+25

Final Answer

x2+25=(x+5*i)*(x−5*i)

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