There are different ways to approach simplifying this expression, but one possible method is to combine the fractions with a common denominator and then factor the resulting quadratic expression. Here are the steps:

1. Find a common denominator for the two fractions in the expression. The least common multiple of the denominators 2 and y^2 is 2y^2, so we can write:

x^2/1 + (1/4)(2y^2)/(2y^2) + (25y^2)/(2y^2) + (16/y^2)/(2y^2) + 2023/1

Simplifying the second fraction, we get:

x^2 + y^2/2 + 25/2 + 8/y^2 + 2023

2. Combine the constant terms:

x^2 + y^2/2 + 2051/2 + 8/y^2

3. Factor the quadratic expression x^2 + y^2/2. This can be done by completing the square or using the formula for the sum of squares:

x^2 + y^2/2 = (x + sqrt(y)/sqrt(2))^2 - y/2

(Note that we chose the positive square root to make the expression simpler.)

4. Substitute this factorization into the expression:

(x + sqrt(y)/sqrt(2))^2 - y/2 + 2051/2 + 8/y^2

5. Simplify and rearrange the terms:

(x + sqrt(y)/sqrt(2))^2 + (8/y^2 - y/2 + 2051/2)

This is a possible simplified form of the expression. Depending on the context or purpose of the expression, it may be useful to further manipulate or evaluate it.