is this formulae in maths which I think I found i.s. (x*x+y*y)=((x*y)*2+((x-y)*(x-y)))already in use?

Question

(x*x+y*y)=((x*y)*2+((x-y)*(x-y)))
for eg:
(4*4)+(3*3)=(3*4*2)+((4-3)*(4-3))
=(12*2)+1
=24+1
=5
my question is that is the above formulae allready established

Answer 1

(x-y) * (x-y) multiplies out as:



x*x - 2*x*y + y*y



So, if you add 2*x*y to that, you get x*x + y*y.



It's a pretty simple "formula".

Answer 2

I think you are trying to ask for the formula :

x^2 + y^2 = 2xy + (x-y)^2

And this can be used by any one.



You have missed ^2 for (x-y) at the end.



The above formula is derived from (x-y)^2 = x^2 + y^2 - 2xy

Here in this formula, -2xy goes to the left hand side then we get

2xy + (x-y)^2 = x^2 + y^2

I think my answer will help to get you out of confusion.

Answer 3

I am unaware of it cause there are lot simple formula like



x*x+y*y=(x+y)(x+y)-2xy



urs is only a derivative of that one

Answer 4

we can use it only when

1)x=y

OR

2)x-y=1

x*x+y*y-2*x*y=(x-y)*(x-y)*(x-y....

(x-y)*(x-y)=(x-y)*(x-y)*(x-y...

=>x-y=0

or

x-y=1