Notice that
x²y⁴ + 2xy² + 1 = (xy²)² + 2xy² + 1²
can be factored as a sum of squares:
x²y⁴ + 2xy² + 1 = (xy² + 1)²
which follows from the identity
(a + b)² = a² + 2ab + b²
with a = xy² and b = 1.
