Question

What is the form of the Pythagorean triple generator?

Answer 1

option-B

Explanation:

We can rewrite left side into right side form

`(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)`

we can expand it

`(x^2+y^2)^2=x^4+x^2y^2+x^2y^2+y^4`

`(x^2+y^2)^2=x^4+y^4+2x^2y^2`

we can add and subtract 2x^2y^2

`(x^2+y^2)^2=x^4+y^4+2x^2y^2+2x^2y^2-2x^2y^2`

`(x^2+y^2)^2=x^4-2x^2y^2+y^4+2x^2y^2+2x^2y^2`

`(x^2+y^2)^2=x^4-2x^2y^2+y^4+4x^2y^2`

`(x^2+y^2)^2=x^4-2x^2y^2+y^4+(2xy)^2`

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