Inequalities

[kaf]

Hi, Can someone please help in explaining this to me.

I saw this question in OG

1-x^2 >= 0

in the answer explanation 1-x^2 was factored to get
(1-x)(1+x)

My question is how do you factor 1-x^2 to get (1-x)(1+x)?

I would be very grateful if someone could explain this to me please.

thanks

[nitya34]

My question is how do you factor 1-x^2 to get (1-x)(1+x)?


well

1-x^2 =(1)^2 - (x)^2= (1-x)(1+x).
got it?

[kaf]

nitya34

I still dont get how 1-x^2 =(1)^2 - (x)^2
because i am thinking ^2 affects only x and not 1

thanks

[nitya34]

a^2-b^2=(a+b)(a-b)

its elementary algebra

just multiply RHS.you will get it

[kaf]

I think i get it now cos 1^2 = 1 anyway so it works it

thanks a lot

[BlindVision]

My question is how do you factor 1-x^2 to get (1-x)(1+x)?


well

1-x^2 =(1)^2 - (x)^2= (1-x)(1+x).
got it?

I thought that this operation would only work if there were brackets enclosing 1 - x such as (1 - x)^2.

Glad I came across this thread to learn something new.