A structural analysis tool uses the expression $(x + 5)^3 - 64x^3$ to compare the load-bearing capacity of two different support beams. To simplify this expression, an engineer applies the difference of cubes factoring pattern: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Match each component of the expression with its correct algebraic base or simplified form.

A manufacturing quality assurance team is analyzing the material required for a new machine bracket. The difference in volume between two cubic sections of the bracket is represented by the expression $(x + 5)^3 - 64x^3$. To simplify the analysis, an engineer needs to factor this expression using the difference of cubes formula: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Which of the following correctly identifies the exact base values, $a$ and $b$, that the engineer must recall to begin applying the formula?

A warehouse manager is analyzing the storage capacity difference between two modular crate designs, represented by the expression $(x + 5)^3 - 64x^3$. To simplify the inventory reports, the manager must factor this expression using the difference of cubes pattern. Arrange the steps of the factoring process in the correct order from start to finish.

An inventory management system uses the expression $(x + 5)^3 - 64x^3$ to model the difference in storage volume between two modular shipping containers. To factor this expression using the pattern $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, an analyst correctly identifies that $a = (x + 5)$. What is the value of $b$ that the analyst must identify to apply the formula correctly?

A logistics coordinator is analyzing the storage capacity difference between two cubic shipping containers, represented by the expression $(x + 5)^3 - {}64x^3$. To factor this expression using the difference of cubes pattern $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, the coordinator recalls that the first binomial factor $(a - b)$ should be written as $((x + 5) - {}4x)$. Is this identification of the first factor correct?

Difference of Cubes Factoring for Storage Capacity

Recalling the Difference of Cubes Pattern for Volumetric Tank Analysis