Question

If we are given a expansion of a identity , can we figure out what identity it is

Answer 1

for example ?

Answer 2

For example like a very big identity like
\[\Huge a^2+b^2+c^2\]

Answer 3

\[\huge a^2 + b^2 + c^2 + 2ab+ 2bc +2ac.\]

Answer 4

This was an example though there are some really big ones

Answer 5

are you asking if we can write it as (a+b+c)^2 without using the identity ?

Answer 6

I mean if you don't know that it boils down to (a+b+c)^2
then how you would you favtor it out

Answer 7

its easy :

a^2 + b^2 + c^2 + 2ab+ 2bc +2ac

(a^2 + b^2 + 2ab) + c^2 + (2bc + 2ac)

(a+b)^2 + c^2 + 2c(a+b)

((a+b) + c)^2

Answer 8

hmm , uh ya , there are some big ones too , i will figure them out ty

Answer 9

bottom line is :

we should memorize formulas by heart so that we can do calculations quickly

also most importantly we should know how to derive them

Answer 10

do you have a proof for (a+b)^2 formula ? or a^3-b^3 formula ?

Answer 11

Proof , is easy lol , just open it

Answer 12

i mean expand

Answer 13

I heard we use binomial..................
for that but i don't know that method
or there are Newton's intepolation blah blah blah