Member • Feb 8, 2012

4_TechHave you ever wondered what is the logic behind equation: (a+b)²=a²+2ab +b² ? This video explains it in very easy to understand language.

Administrator • Feb 8, 2012
Nice! 😀 Has he explained any other formulae in the similar way?4_TechAre you sure? This action cannot be undone. 
Member • Feb 9, 2012
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 ). 😉Are you sure? This action cannot be undone. 
Member • Feb 9, 2012
9 times table on your fingers!
#LinkSnipped#
Mathamagic by bawa!Are you sure? This action cannot be undone. 
Member • Feb 9, 2012
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., (ab)[sup]2[/sup] and (ab)[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 <a href="https://en.wikipedia.org/wiki/Tesseract" target="_blank" rel="nofollow noopener noreferrer">Tesseract</a> or the appropriate hypercube, and it becomes impractical after that..Are you sure? This action cannot be undone. 
Member • Feb 9, 2012
I guess it prompts us to visualise our formule...if i may say so...instead of plain old cramming ...Are you sure? This action cannot be undone. 
Administrator • Jan 5, 2016
We all wish we had such creative teachers in school.Are you sure? This action cannot be undone.