Utkrisht123 Posted March 24, 2013 Report Share Posted March 24, 2013 (edited) All of you know that a^{2 }- b^{2} = (a+b)(a-b) I know only two method to prove it. a^{2 }- b^{2 }a^{2 }- b^{2} a^{2 }- b^{2 }+ ab - ab a^{2 }- b^{2} + 2ab -2ab -2b^{2} a^{2 }+ ab - ab - b^{2 }(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 March 24, 2013 by Utkrisht123 Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted March 24, 2013 Report Share Posted March 24, 2013 Can't you prove it just by expanding the product? All the steps are reversible, so going either direction accomplishes the same thing. Quote Link to comment Share on other sites More sharing options...

0 James33 Posted March 24, 2013 Report Share Posted March 24, 2013 (a+b)(a-b)=a(a-b)+b(a-b)=a^2-ab+ba-b^2=a^2-b^2 Quote Link to comment Share on other sites More sharing options...

0 Prime Posted March 24, 2013 Report Share Posted March 24, 2013 Perhaps, OP is looking for this: Suppose, a = b + k, then k = a - b. a^{2} - b^{2} = (b+k)^{2} - b^{2} = b^{2} + 2bk + k^{2} - b^{2}= k(2b+k) = k(b+k+b)=(a-b)(a+b) Quote Link to comment Share on other sites More sharing options...

0 vinay.singh84 Posted March 25, 2013 Report Share Posted March 25, 2013 a^{2} - b^{2} (a + b - b)^{2} - b^{2} (a + b)^{2 }+ b^{2} - 2b(a + b) - b^{2} (a + b)^{2} - 2b(a + b) (a + b)(a + b -2b) (a + b)(a - b) Quote Link to comment Share on other sites More sharing options...

0 Perhaps check it again Posted January 26, 2014 Report Share Posted January 26, 2014 (edited) 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 January 26, 2014 by Perhaps check it again Quote Link to comment Share on other sites More sharing options...

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## Utkrisht123

All of you know that a

^{2 }- b^{2}= (a+b)(a-b)I know only two method to prove it.

a

^{2 }- b^{2 }a^{2 }- b^{2}a

^{2 }- b^{2 }+ ab - ab a^{2 }- b^{2}+ 2ab -2ab -2b^{2}a

^{2 }+ ab - ab - b^{2 }(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## Link to comment

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