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


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5 replies to this topic

#1 Utkrisht123

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Posted 24 March 2013 - 03:57 AM

All of you know that a- b2 = (a+b)(a-b)

I know only two method to prove it.

  a- b2                                                                               a- b2

  a- b2  + ab - ab                                            a- b2 + 2ab -2ab -2b2

 a2 + ab - ab - b2                                                           (a+b)2 - 2b(a+b)

 a(a+b) - b(a+b)                                              (a+b)(a+b) - 2b(a+b) 

 (a-b)(a+b)                                                      (a+b)(a+b-2b)

                                                                        (a+b)(a-b)

 

Apart form these two method are there any other method to prove it.

  


Edited by Utkrisht123, 24 March 2013 - 03:59 AM.

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#2 bonanova

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Posted 24 March 2013 - 04:13 AM

Can't you prove it just by expanding the product?
All the steps are reversible, so going either direction accomplishes the same thing.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 James33

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Posted 24 March 2013 - 08:11 PM

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


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#4 Prime

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Posted 24 March 2013 - 11:37 PM

Perhaps, OP is looking for this:

Spoiler for a - b

 


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Past prime, actually.


#5 vinay.singh84

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Posted 25 March 2013 - 06:49 PM

Spoiler for

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#6 Perhaps check it again

Perhaps check it again

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Posted 26 January 2014 - 06:47 AM

In post # 1 in the right-hand column under

 

"a^2 - b^2,"

 

the next line should be

 

"a^2 + b^2 + 2ab - 2ab - 2b^2."


Edited by Perhaps check it again, 26 January 2014 - 06:51 AM.

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