1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Proof for one-to-one function

  1. Jan 5, 2013 #1
    Please may someone explain the last step of this proof for me? I can't see how it's done algebraically. Where does the second (x1-x2) go? Is it a mistake?


    I've tried multiplying out -2 and everything else I could think of but to no avail.

    Thank you.
  2. jcsd
  3. Jan 5, 2013 #2
    Hi chickensagan.
    There is no error, this is just factorization.
    maybe you are being intimidated by the (x2-x1) expression, just call it 'a'. and call 'x1+x2' 'b'
    so in the last step you have a.b - 2.a = a(b-2)
    Not sure if I really addressed your problem.

  4. Jan 5, 2013 #3
    Thanks for the reply Oli4, but I still don't get it.
    I don't understand how they factorise it when both sides don't have 2 as a common factor, and even if that happened how does the -2 end up inside the bracket?
  5. Jan 5, 2013 #4
    what is being factorized is the term (x2-x1) or the term 'a' in my simplified version.
    a*b+a*2=a*(b+2) <- is this problematic for you ? just check it by doing the expansion.
    in this case it is a*b-a*2=a*(b-2)
    with a being x2-x1 and b being x2+x1
  6. Jan 5, 2013 #5


    User Avatar
    Gold Member

    Perhaps more simply:$$(x_1 - x_2)(x_1 + x_2) - 2(x_1 - x_2) = (x_1 - x_2)[(x_1 + x_2) - 2].$$Using the [,] might make you see it easier - I just used a common factor of ##(x_1 - x_2)##.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook