How do you factor x^2+36y^2?

Jan 5, 2017

A sum of two squares cannot be factored using real numbers.

Explanation:

In order to factor ${a}^{2} + {b}^{2}$, we need to think of it as

${a}^{2} - \left(- {b}^{2}\right)$.

Then we can factor using imaginary numbers:

${a}^{2} - \left(- {b}^{2}\right) = \left(a + b i\right) \left(a - b i\right)$ where ${i}^{2} = - 1$.

So

${x}^{2} + 36 {y}^{2} = \left(x + 6 y i\right) \left(x - 6 y i\right)$ where ${i}^{2} = - 1$.