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Homework Help: Show that (2a-1)^2 - (2b-1)^2 = 4(a-b)(a+b-1)

  1. Mar 7, 2007 #1
    hope you can help, thnx

    1. The problem statement, all variables and given/known data

    Show that (2a-1)^2 - (2b-1)^2 = 4(a-b)(a+b-1)

    2. Relevant equations

    n/a

    3. The attempt at a solution

    I thought that i needed to rearrange (2a-1)^2 - (2b-1)^2 to show 4(a-b)(a+b-1)


    my attempt...

    4a^2 - 4a + 1 - 4b^2 - 4b + 1
    4(a^2 - a + (1/4) - b^2 - b + (1/4))
    4(a^2 - a - b^2 - b + (1/2))

    then i turnt that to this which i really think is going the wrong direction lol

    4(a(a-1)-b(b+1)+(1/2))

    lol

    anyways, if i was to try and solve my errors myself id tell myself to try and extract the (a-b) as a factor from 4(a^2 - a + (1/4) - b^2 - b + (1/4))

    hope you can help

    thnx
     
  2. jcsd
  3. Mar 7, 2007 #2
    Look at your first step.

    4a^2 - 4a + 1 - 4b^2 - 4b + 1

    Can you see the mistake? Use brackets to expand (2a-1)^2 - (2b-1)^2! :)

    Tell me if you need more help, I will be glad to help. (or if I am offline, someone else will)
     
    Last edited: Mar 7, 2007
  4. Mar 7, 2007 #3
    note that a - [b - a] = a -b + a = 2a-b

    After you figure that part out, just expand this : 4(a-b)(a+b-1) and you will see similarities between what you have and what they want .
     
  5. Mar 7, 2007 #4
    i may be wrong, but is (2a-1)^2 - (2b-1)^2

    4a^2 - 4a + 1 - 4b^2 + 4b - 1 ???

    thnx for the help
     
  6. Mar 7, 2007 #5
    Yes, you are correct there.

    So now simplify it to [tex] 4a^{2} - 4a -4b^{2}+4b[/tex]

    Now what is 4(a-b)(a+b-1) once you expand it.
     
    Last edited: Mar 7, 2007
  7. Mar 7, 2007 #6
    o rite sweet, i got it :D

    thnx buddy for the help
     
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