The problem
FACTORING DIFFERENCE OF TWO SQUARES
Hello ,the equation x^4 -1 ,how did they get 3 terms (x-1)(x+1)(x^2+1) as an answer ?
I thought it would've been (x^2-1)(x^2 -1 )
the 1st step they calculated
(x^2-1)(x^2 -1 )
then some way or another they calculated
(x^2-1^2)(x^2 -1 ) ... how did they get a 1^2 ?
I thought it would've just been 1 ... thank you .
Answer provided by our tutors
>I thought it would've been (x^2-1)(x^2 -1 )
This is incorrect. x^4-1 is a difference of squares --- (x^2)^2 - 1^2.
The formula for factoring the difference of squares is a^2-b^2=(a-b)(a+b) -- so one of your terms will have a '+' sign.
Then there is a second factoring step because x^2-1 is also a difference of sqaures
1 is equal to 1^2 -- we just write it in that way so that it is more obvious that there is a square there.