Factor a^2+b^2

Problem

a^2+b^2

Solution

1. Identify the expression as a sum of squares, which does not have a simple factorization using real numbers.

2. Apply the imaginary unit i where i^2=−1 to rewrite the expression as a difference of squares.

3. Rewrite the expression by changing the addition to the subtraction of a negative value: a^2−(−b^2)

4. Substitute −b^2 with (b*i)^2 to obtain the form a^2−(b*i)^2

5. Factor using the difference of squares formula x^2−y^2=(x−y)*(x+y) where x=a and y=b*i

Final Answer

a^2+b^2=(a+b*i)*(a−b*i)

Want more problems? Check here!