Question

Quick question: Why can't you factor the "sum of two squares"? Please make it simple... ^-^ Thanks!! (I'm just curious.)

Answer 1

Because you have to have that third term of:

2xy

That's if you wanted to factor:

x^2 + y^2

You can't because you need that 2xy :

x^2 + 2xy + y^2 = (x + y)(x + y) = (x + y)^2

Answer 2

All good now, @ashizepic ?

Answer 3

You would otherwise have to start with:

(x + y)(x + y)

or

(x - y)(x - y)

to keep that sign positive in "the sum of 2 squares" and either of these produces a third term.

Unlike:

(x + y)(x - y) = x^2 - y^2

where you can have the difference of 2 squares because here, that third term vanishes.

That's a little bit more explanation. But you wanted it short initially.

Answer 4

you can factor the sum of 2 squares ... but it depends on what type of solutions you are looking for

Answer 5

Yes, if you allow complex numbers.

Answer 6

Ohhh... thank you!

Answer 7

uw!