Question

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 can factor a difference of two squares like so: \[\large a^2 - b^2 = (a+b)(a-b)\]

Unless you've learned complex/imaginary numbers, you can't factor a sum of two squares. If you have learned them, http://www.coolmath.com/algebra/10-complex-numbers/02-factoring-the-sum-of-two-squares-01.htm