In a technical design scenario, you are simplifying a formula for the area of a specialized component represented by the expression ${}4a^5b - 64ab$. Arrange the following steps in the correct order to factor this expression completely.

A quality assurance technician is reviewing a software algorithm that calculates the structural tolerance of a manufactured metal beam. The original equation includes the polynomial expression ${}4a^5b - 64ab$. To optimize the software's processing speed, the technician needs to replace the expression with its completely factored form. Which of the following represents the correct completely factored form that the technician should input?

A quality assurance supervisor is verifying the mathematical breakdown of a material stress formula, ${}4a^5b - 64ab$, for a new technical manual. Match each mathematical component of the factoring process with its correct value as described in the simplification steps.

A manufacturing technician is simplifying the expression ${}4a^5b - 64ab$ to model the stress on a specialized component. During the factoring process, the technician reaches the form ${}4ab(a - 2)(a + 2)(a^2 + 4)$. True or False: This expression is considered 'completely factored' over the set of real numbers because the binomial $(a^2 + 4)$ cannot be factored further.

Initial Factoring Component for Production Formulas

Documenting Polynomial Simplification Steps

In a supply-chain distribution center, a logistics coordinator uses an optimization formula to model the storage capacity of nested shipping containers. The raw capacity variance between two container lines is modeled by the expression ${}4a^5b - 64ab$. To analyze the structural scaling, the training manual instructs the coordinator to factor the expression completely, starting by extracting the greatest common factor (GCF).

Fill in the blank with the greatest common factor of the terms in the expression:

The greatest common factor is ____.