Geometric proofs : a² -b²; (a+b)²

[CS227]

Geometric proofs : a² -b²; (a+b)²

Hi, I need the geometric proof of a² -b² and (a+b)². Could somebody please post a link to a site where I can find it, or tell me how to do it ?

 

[galactus]

Here's a nice little proof of the difference of two squares:

The dimensions of 1 are a and a-b. The area of 1 is a(a-b), and the area

of 2 is b(a-b).

The area \(\displaystyle A=a^{2}-b^{2}=a(a-b)+b(a-b)=(a+b)(a-b)=a^{2}-b^{2}\)

Rather simple. See?.

 

[soroban]

The one for \(\displaystyle (a\,+\,b)^2\) is even nicer . . .

            a         b
      * - - - - - * - - - *
      |           |       |
      |           |       |
    a |     a²    |   ab  | a
      |           |       |
      |           |       |
      |           |       |
      * - - - - - + - - - *
      |           |       |
    b |    ab     |   b²  | b
      |           |       |
      * - - - - - * - - - *
            a         b

Therefore: \(\displaystyle \,(a\,+\,b)^2\;=\;a^2\,+\,2ab\,+\,b^2\)

*

 

[CS227]

Thank you so much !!!