Question

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

Answer 1

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-(-b^2)`.

Then we can factor using imaginary numbers:

`a^2-(-b^2) = (a+bi)(a-bi)` where `i^2 = -1`.

So

`x^2+36y^2 = (x+6yi)(x-6yi)` where `i^2 = -1`.