Subtracting $(a^2 + 5ab - 6b^2)$ from $(a^2 + b^2)$

Subtracting $(m^2 - 7mn - 3n^2)$ from $(m^2 + n^2)$

As part of developing an automated financial tracking tool, you are required to document the exact algebraic steps taken to subtract the old cost model, $(p^2 + 10pq - 2q^2)$, from the new baseline model, $(p^2 + q^2)$. Recall the standard procedure for polynomial subtraction and arrange the computational steps in the correct operational order.

A logistics company uses two different models to estimate operational costs. Model A is represented by the polynomial $p^2 + q^2$, and Model B is represented by $p^2 + 10pq - 2q^2$. If an analyst subtracts Model B from Model A to find the difference, which simplified expression represents the result?

A corporate data analyst is verifying the sign changes in a financial model used for budget forecasting. The model requires subtracting the 'Expense Projection' polynomial $(p^2 + 10pq - 2q^2)$ from the 'Revenue Baseline' polynomial $(p^2 + q^2)$. Match each original term from the Expense Projection polynomial with its correct form after the subtraction sign has been distributed (but before combining like terms).

In a corporate financial forecasting tool, the efficiency variance is calculated by subtracting the 'Operational Risk' polynomial $(p^2 + 10pq - 2q^2)$ from the 'Planned Revenue' polynomial $(p^2 + q^2)$. During the algebraic process of subtracting these two polynomials, the distributive property is applied to the 'Operational Risk' polynomial, which results in the $-2q^2$ term becoming positive.

An inventory analyst is auditing a database formula and must subtract the 'Shrinkage' model, $(p^2 + 10pq - 2q^2)$, from the 'Total Stock' model, $(p^2 + q^2)$. Recalling the proper algebraic rules for polynomial subtraction, the analyst begins by distributing the subtraction operation. This step is performed by multiplying each term in the 'Shrinkage' model by ____, which correctly changes their signs before combining like terms.