Use the Pythagorean identity, Latex: (x^2-y^2)^2+(2xy)^2=(x^2+y^2)^2\tex tsf{,} to create a Pythagorean triple. Follow these steps:

Choose two numbers and identify which is replacing Latex: x
x
and which is replacing Latex: y\textsf{.}

How did you know which number to use for Latex: x
x
and for Latex: y\textsf{?}

Explain how to find a Pythagorean triple using those numbers.

Explain why at least one leg of the triangle that the Pythagorean triple represents must have an even-numbered length.