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Add the two like monomials:

$$25y^2 + 15y^2$$

Both terms contain the same variable $$y$$ raised to the same exponent $$2$$, so they are like terms. Combine them by adding the coefficients: $$25 + 15 = 40$$, while the variable part $$y^2$$ remains unchanged:

$$25y^2 + 15y^2 = 40y^2$$

This example illustrates the simplest case of monomial addition: when two monomials share the same variable and exponent, just add their numerical coefficients and keep the variable factor as is.

Adding $$25y^2 + 15y^2$$

A logistics coordinator is merging two operational datasets for a monthly report. Dataset A has a value represented by the expression $$25y^2$$ and Dataset B has a value of $$15y^2$$. What is the resulting simplified expression for the total value of these two datasets, and what is the mathematical rule regarding the exponent of the variable $$y$$ during this specific addition process?

Consolidating Operational Unit Estimates

Based on the rules for adding monomials, state the two specific criteria (regarding the variable and the exponent) that must be met for $25y^2$ and $15y^2$ to be classified as like terms. Additionally, describe the mathematical procedure used to handle the numerical coefficients and the variable parts to arrive at the total of $40y^2$.

Auditing Automated Resource Consolidation

In your role as a technical documentation specialist, you are updating a training manual for data analysts. You need to describe the specific mathematical procedure for adding the terms $25y^2$ and $15y^2$. In your response, clearly state which components of these monomials are added together, explain what happens to the variable $y^2$ during the process, and provide the final simplified result.

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