does (s+1)^2 factor to s^2 + 1 ?

Question

i feel retarded for forgetting this. also if anyone has a similiar answer to what x^2 + 4 factors to, for real numbers, if at all. just checkin

thanks!!!

Answer 1

Actually what you are doing is expanding (s+1)², not factoring. You always expand using FOIL:

(s + 1)² = (s + 1)(s + 1)
First: s²
Outer: s
Inner: s
Last: 1

So this expands to s² + 2s + 1

When *factoring*, you can only do something if you have a *difference* of squares. Thus, you can't do anything with x² + 4 (without getting into imaginary numbers)...

On the other hand if you had a *difference* of squares, then you could do something.

x² - 4 = (x + 2)(x - 2)

Notice how the signs are different... when you expand this it becomes x² + 2x - 2x - 4 and the 2x and -2x cancel out. This leaves x² - 4. The same thing *doesn't* work for a sum of squares.

Answer 2

u can do foil (first, outside, inside, last) to multiply them

(s+1)^2 = (s+1)(s+1) = s^2+2s+1
for the second one,
x^2+4 cannot be factored any more because they don't have any common factors (i think)

Answer 3

No!!!!! (s+1)^2 if we want to factored it become

(s+1)(s+1)

Answer 4

No:
(s+1)^2 = s^2+2s+1

for x^2+4 this is

x^2-(2i)^2 where i is square root of -1

= (x+2i)(x-2i)

Answer 5

no.itfactorsto (s+1)(s+1)