How do you find the sum of two squares?
Is finding the sum of two squares just finding the perfect square?

I have to answer this 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.

All I have is:
Contrast - You can't factor the sum of two squares, but you can factor the difference.

Compare - Before you can find the difference of sum of two squares, the equation must have a perfect square.

Could u show an example?

Question

How do you find the sum of two squares? 
Is finding the sum of two squares just finding the perfect square?

I have to answer this 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.
 
All I have is: 
Contrast - You can't factor the sum of two squares, but you can factor the difference.

Compare - Before you can find the difference of sum of two squares, the equation must have a perfect square.

Could u show an example?

anonymous · Answer

the sum of two squares does not have real solutions

campbell_st · Answer

an example of the difference of 2 squares is 

x^2 - 16

the sum of 2 squares is 

x^2 + 16

which won't factor. 

If you where solving, then you could complete the square... 

but as @Luis_Rivera says... it will have complex roots.

anonymous · Answer

So if you have x^2 + 25 the factor couldn't be (x + 5)(x + 5) , it would just be prime?

mathstudent55 · Answer

Correct. x^2 + 25 is prime.
x^2 - 25, on the other hand, factors into (x + 5)(x - 5)