As an inventory specialist, you calculate the combined volume of two different sections of cubic storage bins, resulting in the expression ${}24x^3 + 81y^3$. To identify the individual dimensions of the bins, you must factor this mathematical model completely. Recalling the process of factoring out the greatest common factor and the sum of cubes pattern, which of the following is the completely factored form?

A shipping logistics company uses two different sizes of cubic containers. The combined volume of these containers is expressed as ${}24x^3 + 81y^3$. To better organize the warehouse space, a manager needs to factor this expression. Match each part of the factoring process to its corresponding mathematical value or term.

A kitchen designer is calculating the total volume for two different sizes of custom cubic cabinets, modeled by the expression ${}24x^3 + 81y^3$. To finalize the dimensions, the designer must factor the expression completely. Arrange the steps of the factoring process in the correct order.

A logistics coordinator is factoring the expression ${}24x^3 + 81y^3$ to determine dimensions for a shipping container. After extracting the greatest common factor of 3 and identifying $a = 2x$ and $b = 3y$ for use in the sum of cubes pattern, the coordinator must write the first factor, $(a + b)$. This linear binomial factor is ____.

In a warehouse management system, the combined capacity of two cubic storage zones is modeled by the expression ${}24x^3 + 81y^3$. A maintenance technician records the completely factored form of this capacity as ${}3(2x + 3y)(4x^2 + 6xy + 9y^2)$. This database entry is mathematically correct.