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

1 Answer
Jan 5, 2017

Answer:

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#.