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

The difference of two squares can be factored as follows:\[a^2-b^2=(a+b)(a-b).\]But I'm not sure whether\[a^2+b^2\]is factorisable at all. :/

Answer 2

You could write\[(a+b)^2-2ab,\]but I'm not sure whether that counts as a true factorization or not.

Answer 3

a^2+b^2 is not factorable further.