Essay

Factoring Warehouse Capacity Models

As a trainee in a logistics company, you are helping design a spreadsheet that models warehouse capacity sharing between two regional hubs, Hub A and Hub B. The total shared storage footprint is represented by the algebraic expression a211ab+10b2a^2 - 11ab + 10b^2, where aa is the capacity factor of Hub A and bb is the capacity factor of Hub B. To simplify the database queries, the engineering team needs to store this formula in its factored form.

In your training journal, write a short essay explaining how to factor the expression a211ab+10b2a^2 - 11ab + 10b^2 step-by-step. In your explanation, you must:

  1. Explain how you determine the signs (positive or negative) of the coefficients in the binomial factors based on the signs of the middle term and the last term.
  2. State the negative factor pairs of the constant coefficient 10.
  3. Identify which specific factor pair adds up to the middle term coefficient of -11, and write the final factored expression.

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Updated 2026-06-18

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