A facility maintenance supervisor is calculating the volume of liquid in two storage tanks, modeled by the expression ${}6x^3y + 48y^4$. To simplify the maintenance logs, the supervisor needs to factor the expression completely. Match each part of the factoring process to its corresponding mathematical expression.

A project coordinator is calculating the total volume of two modular office units, which is represented by the expression ${}6x^3y + 48y^4$. To simplify the architectural plans, the coordinator must first identify the greatest common factor (GCF) of the two terms. Which of the following is the GCF of ${}6x^3y$ and ${}48y^4$?

A quality control inspector is simplifying a formula for the density of two composite materials, represented by the expression ${}6x^3y + 48y^4$. After factoring out the greatest common factor of ${}6y$, the inspector identifies the remaining binomial $x^3 + 8y^3$ as a sum of two perfect cubes, $(a)^3 + (b)^3$. In this scenario, what is the term that represents the value of $b$?

A manufacturing supervisor is calculating the volume of two custom engine parts, which is represented by the algebraic expression ${}6x^3y + 48y^4$. To simplify the design specifications for the production team, the supervisor needs to factor this expression completely. Arrange the steps of the factoring process in the correct order.

Factoring Volume Expressions in Manufacturing

Simplifying Storage Space Calculations in Logistics