Why couldn't this be factored further?

[Peter Tran]

Homework Statement

Factor the following difference of two squares. Assume that variables represent whole numbers.

s^4 - 625

Homework Equations

(A)^2 - (B)^2

The Attempt at a Solution

s^4-625
(s^2)^2 - 25^2
(s^2+25)(s^2-25)
(s^2+25)(s+5)(s+5) - Correct

The "program" wants me to stop there, but why? Couldn't I just go ahead and continue factoring the (s^2+25) also?

 

[Mentallic]

You can't factor a²+b². You were able to factor difference of two squares only, not sum of two squares.

p.s. I think you made a typo, it should be (s²+25)(s+5)(s-5)

 

[eumyang]

Homework Statement

Factor the following difference of two squares. Assume that variables represent whole numbers.

s^4 - 625

Homework Equations

(A)^2 - (B)^2

The Attempt at a Solution

s^4-625
(s^2)^2 - 25^2
(s^2+25)(s^2-25)
(s^2+25)(s+5)(s+5) - Correct

The "program" wants me to stop there, but why? Couldn't I just go ahead and continue factoring the (s^2+25) also?

No. There is no way to factor s² + 25 (or any sum of two squares in the form a² + b²) under the real numbers. However, if you are familiar with complex numbers, then s² + 25 could be factored further, but I don't know if you need to do that.

 

[Peter Tran]

Oh that's right, I completley forgot that I could only factor A² - B².
Thanks.