I'm sorry, but that is not true for all values of x and y

It is true when x and y are both 0, and for certain irrational
numbers.  But for instance if

     x=2 and y=1

Substitute in

    9x²y² = 9y²+x²

9(2)²(1)² = 9(2)²+(2)²
  9(4)(1) = 9(4)+4
       36 = 36+4
       36 = 40

which is false.

Edwin

However if you eliminate the + sign on the right
and make it multiplication instead:

(3xy)² = 9y²x² ,

then it will be true

Here is why that will be true:

(3xy)² = (3xy)(3xy) = 3·x·y·3·x·y = 3·3·y·y·x·x = 9y²x²

Edwin