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.

A warehouse manager is evaluating an expression for the total volume of two joined storage sections, given by ${}6x^3y + 48y^4$. The completely factored form of this expression is ${}6y(x + 2y)(x^2 + 2xy + 4y^2)$.