To factor the expression ${}2p^3 + 54q^3$ completely, arrange the following steps in the correct logical order.

In technical fields such as advanced manufacturing, simplifying polynomial expressions is a common step in optimizing design formulas. Suppose a volume calculation formula involves the expression ${}2p^3 + 54q^3$. To simplify it completely, you must first factor out the greatest common factor and then recall the exact structure of the 'sum of cubes' pattern. Which of the following represents the completely factored form of this expression?

In a logistics design project, you are asked to simplify the material volume expression ${}2p^3 + 54q^3$ by factoring it completely. Match each component of the factoring process with its correct value.

To factor the expression ${}2p^3 + 54q^3$ completely, the first step is to factor out the greatest common factor of ${}2$.

Identifying Factor Components in Design