Question about counterexample

Question

How do I show by counterexample that (x+y)^-^2 and x^2 + y^2 are not equivalent?

Answer 1

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

 

Let x = 1, y = 2, then

 

(1+2)^(-2) =? 1^2 + 2^2

 

3^(-2) =? 1 + 4

 

1/9 ≠ 5

Answer 2

It seems this was :

 

   ( X + y ) ^2     and X^2 + Y^2

 

   Students always make a mistake, and let those 2 expressions equal:

 

       ( X +y ) ^2 = ( X+ y ) ( X+y) =( X+ Y ) X + (X+Y ) Y

 

                                                   = X^2 + XY + XY + Y^2 = X^2 + 2XY + Y^2

 

     

Answer 3

^{Notice that (2+3)^(-2) is not equal to 2^(2)+3^(2)}