A mechanical engineer is simplifying a formula for the volume of a machine part, expressed as ${}40x^2y + 44xy - 24y$. According to the standard factoring process, what is the greatest common factor (GCF) that should be extracted from the expression first?

A structural engineering technician is evaluating a load-bearing formula represented by the expression ${}40x^2y + 44xy - 24y$. The completely factored form of this expression is ${}4y(10x^2 + 11x - 6)$.

An inventory manager is using the algebraic expression ${}40x^2y + 44xy - 24y$ to model the fluctuating costs of warehouse storage. To simplify the expression for a report, they need to factor it completely. Match each component identified during the factoring process with its correct mathematical representation.

An operations manager is using the formula ${}40x^2y + 44xy - 24y$ to model production efficiency across different shifts. To make the formula easier for the shift leads to use, the manager decides to factor it completely. Arrange the following steps in the order the manager should perform them to arrive at the simplified version of the formula.

Simplifying a Resource Allocation Model

A logistics coordinator is working with an optimization model where the total material cost is given by the expression ${}40x^2y + 44xy - 24y$. To simplify the model for their team's software tool, they need to factor it completely. The first step is to identify and extract the greatest common factor (GCF). The GCF of this expression is ____.