Question

There is a nice simple pattern for factoring the difference of two squares. Explain why the sum of two squares is not factorable in this way.

Answer 1

When you take the difference of two squares and factor it, the two middle terms cancel each other out. There is no comparable result that will give the sum of two squares.

Answer 2

when you have the sum of 2 squares you have a middle term
with the difference of 2 squares the 2 middle terms cancel out

(a + b)^2 = a^2 + ab + ba + b^2
ab = ba
therefore (a + b)^2 = a^2 + 2ab + b^2

(a -b)^2 = a^2 -ab + ab + b^2 -ab + ab = 0
therefore (a+b)^2 = a^2 - b^2

Answer 3

thanks, both of you.

Answer 4

welcome