As a logistics planner calculating the dimensions of custom shipping crates for an industrial warehouse, you are given the surface area expression ${}8x^2y - 24xy + 18y$. To find the exact length and width multipliers for your crates, you must factor this expression completely. Recalling the step-by-step process of first factoring out the greatest common factor (GCF) and then identifying perfect square trinomials, which of the following represents the completely factored form?

In a manufacturing plant, the surface area of a customized metal bracket is represented by the expression ${}8x^2y - 24xy + 18y$. To determine the production dimensions, you must factor this expression completely. Arrange the following steps in the correct order to recall the standard factoring process for this expression.

A facility manager is calculating the required floor space for a new modular storage layout using the area expression ${}8x^2y - 24xy + 18y$. To standardize the procurement specs, the manager must identify the mathematical components of the factored form. Match each component of the factoring process with its correct term.

A production supervisor at a textile mill is reviewing a formula for fabric waste: ${}8x^2y - 24xy + 18y$. True or False: According to the standard factoring process, the first step to factor this expression completely is to extract the greatest common factor (GCF), which is ${}2y$.

GCF Identification in Industrial Modeling

A sheet metal fabrication technician is determining the dimensions of a custom square-based ventilation duct. The cross-sectional area of the duct is represented by the algebraic expression ${}8x^2y - 24xy + 18y$. To find the dimensions, the technician first factors out the greatest common factor (GCF) of ${}2y$ to get ${}2y(4x^2 - 12x + 9)$. To finalize the dimensions, the technician must recall the perfect square trinomial pattern to factor the remaining part, ${}4x^2 - 12x + 9$, as the square of a single binomial. What is the binomial that, when squared, equals ${}4x^2 - 12x + 9$? (Write your answer in the standard form $ax - b$, with no parentheses or exponents, using spaces around the operator: ____ )

Explaining the Factoring Process for Custom Column Estimation