In a manufacturing analysis, the difference in the volume of two containers is represented by the expression $(n + 3)^3 - 125n^3$. To factor this expression using the pattern $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, which of the following correctly identifies the values that should be used for $a$ and $b$?

An operations manager is analyzing a volume difference expression, $(n + 3)^3 - 125n^3$, to optimize storage space. To factor this expression using the difference of cubes identity $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, match each formula component with its correct algebraic representation.

A data analyst is simplifying a capacity model represented by the expression $(n + 3)^3 - {}125n^3$. True or False: When applying the difference of cubes identity $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, the middle term of the trinomial factor, $ab$, is correctly represented by the product $(n + 3)({}5n)$.

Logistics Capacity Modeling

A supply chain analyst needs to simplify a capacity difference model, represented by the expression $(n + 3)^3 - 125n^3$. Recall the algebraic procedure for factoring the difference of cubes. Arrange the steps required to factor this expression completely into the correct sequential order.

Analyzing Storage Capacity with Difference of Cubes