Factor x^2+8

Problem

x2+8

Solution

1. Identify the type of expression. This is a sum of squares in the form a2+b2 where a=x and b=√(,8)=2√(,2)

2. Apply the complex factoring rule for the sum of squares, which states a2+b2=(a+b*i)*(a−b*i)

3. Substitute the values a=x and b=2√(,2) into the formula.

4. Simplify the expression to show the factors using the imaginary unit i

Final Answer

x2+8=(x+2*i√(,2))*(x−2*i√(,2))

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