A facility manager is calculating the total storage area of a new warehouse wing, which is represented by the algebraic expression $ab + 7b + 8a + 56$. To simplify the architectural plans, the manager needs to factor this expression completely using the grouping method. Which of the following represents the correct factored form of the area?

As an operations analyst, you are simplifying a formula used to calculate total warehouse space: $ab + 7b + 8a + 56$. You need to factor this expression by grouping to optimize your spreadsheet calculations. Arrange the following steps of the factoring by grouping process in the correct sequence from start to finish.

A logistics coordinator is simplifying a warehouse storage capacity formula, $ab + 7b + 8a + 56$, to create a more efficient inventory spreadsheet. Match each component of the factoring by grouping process with its correct algebraic representation.

An operations manager is analyzing a staffing model represented by the polynomial $ab + 7b + 8a + 56$. When this expression is completely factored using the grouping method, one of the resulting binomial factors is $(a + 8)$.

Factoring Warehouse Floor Plans

A logistics coordinator at a distribution center is simplifying a warehouse floor plan area represented by the polynomial expression $ab + 7b + 8a + 56$. By grouping the terms, the coordinator rewrites the area formula as $b(a + 7) + 8(a + 7)$. To find the completely factored form, the coordinator factors out the common binomial factor $(a + 7)$, which results in $(a + 7)$ multiplied by another binomial. What is this second binomial factor? (Do not include any spaces in your answer, e.g., write as $b+8$ or $(b+8)$.)