(a+b)²=a²+2ab +b²... But Why??? Now Explained! Do Watch!

Replies

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  Ankita Katdare

  4_Tech

  Nice! 😀 Has he explained any other formulae in the similar way?
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  circularsquare

  That is one nice way to remember.
  But the formula comes from the commutative ,distributive laws of addition and multiplication.
  Commutative Law - ab = ba and a + b = b + a
  Distributive Law - a(b + c) = ab + ac .
  
  Thus ,(a + b)^2 = (a + b) (a + b) --- by the definition of power of 2
  = a(a + b) + b(a + b) --- by distributive law
  = aa + ab + ba + bb --- by distributive law
  = a^2 + ab + ba + b^2 ---by definition of power of 2
  = a^2 + ab + ab + b^2 ----by commutative law of multiplication
  = a^2 + 2ab + b^2
  
  So there , I robbed all the fun out of it.
  
  😛
  *This was a sarcastic post intended to provide humorous relief - I know everyone knows above derivation.*
  
  Sometimes I wonder whether mathematics is anything more than a bunch of definitions and the law of identity (i.e A = A ). 😉
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  4_Tech

  9 times table on your fingers!
  
  #-Link-Snipped-#
  
  Mathamagic by bawa!
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  silverscorpion

  I tried the same for (a+b)[sup]3[/sup]
  
  Here, of course, instead of a square, we have to use a cube. And sure enough, the total volume (instead of area) of the cube comes to be
  
  (a+b)[sup]3[/sup] = a[sup]3[/sup] + b[sup]3[/sup] + 3a[sup]2[/sup]b + 3ab[sup]2[/sup]
  
  You can also use it to get the formula of squares and cubes of differences, ie., (a-b)[sup]2[/sup] and (a-b)[sup]3[/sup]. Just that, in the square or the cube, instead of having the total length as (a+b), keep the total length as a, and have another segment b in it. Compute the required area or volume, and it comes to be correct.
  
  Now, this will prove to be a little bit more difficult if we go to more number of variables, like (a+b+c)[sup]2[/sup] or (a+b+c)[sup]3[/sup], as we will have more rectangles or more cubes to compute the area or volume.
  
  Also, when the power goes beyond 3, we will have to imagine a Tesseract or the appropriate hypercube, and it becomes impractical after that..
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  4_Tech

  I guess it prompts us to visualise our formule...if i may say so...instead of plain old cramming ...
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  Ankita Katdare

  We all wish we had such creative teachers in school.