Using complete sentences, compare and contrast the ways to factor the "sum of two squares" and the "difference of two squares." Provide an explanation and example of each, including any similarities and differences.

Question

sburchette · Answer

A sum of two squares has no solutions in the set of real numbers. It can only have imaginary roots. Ex/$$x^2+1=(x+i)(x-i)$$ Where i=sqrt(-1)
 A difference of two square can be written as (x+a)(x-a) where a is the sqrt of the original constant. Ex/$$x^2-4=(x+2)(x-2)$$