Question

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.

Answer 1

you cannot factor the sum of two squares , at least not with real numbers

Answer 2

the difference of two squares factors as
\[a^2-b^2=(a+b)(a-b)\] so for example
\[x^2-16=(x+4)(x-4)\] but \(a^2+b^2\) does not factor, so for example you cannot factor
\[x^2+16\]