Question

2xy^2 + x^2y^4 +1 = ??
Pls worth 100 POINTS :

Answer 1

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.