1Cademy - Finding the Difference $$(9b^2 - 5b - 4) - (3b^2 - 5b

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Adding and Subtracting Polynomials

Example

Finding the Difference $(9b^2 - 5b - 4) - (3b^2 - 5b - 7)$

Find the difference of the polynomials:

$(9b^2 - 5b - 4) - (3b^2 - 5b - 7)$

First, distribute the subtraction by changing the sign of every term in the second polynomial:

$9b^2 - 5b - 4 - 3b^2 + 5b + 7$

Next, rearrange the terms to group the like terms together:

$9b^2 - 3b^2 - 5b + 5b - 4 + 7$

Finally, combine the like terms. Notice that $-5b + 5b = 0$ , so the $b$ -term is eliminated:

$6b^2 + 3$

Updated 2026-05-25

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OpenStax Intermediate Algebra

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Intermediate Algebra @ OpenStax

Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax

Algebra

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Your company's finance team models quarterly revenue using the expression ${}9b^2 - 5b - 4$ and quarterly expenses using ${}3b^2 - 5b - 7$ . To report the projected profit, you must find the difference between revenue and expenses by evaluating $(9b^2 - 5b - 4) - (3b^2 - 5b - 7)$ . Arrange the steps in the correct order to simplify this expression.
A logistics coordinator uses the expression ${}9b^2 - 5b - 4$ to represent the operational costs of Route A and ${}3b^2 - 5b - 7$ for Route B. To calculate how much more expensive Route A is than Route B, the coordinator evaluates $({}9b^2 - 5b - 4) - (3b^2 - 5b - 7)$ . Based on the simplification steps for this expression, what is the final simplified form?
A project manager at a manufacturing firm is comparing two cost-efficiency models represented by polynomials: Model A is ${}9b^2 - 5b - 4$ and Model B is ${}3b^2 - 5b - 7$ . To calculate the difference between the two models, the manager evaluates $({}9b^2 - 5b - 4) - ({}3b^2 - 5b - 7)$ . Match each stage of the simplification process with its correct mathematical result.
A project manager is calculating the difference between two quarterly cost-efficiency models represented by the polynomials $(9b^2 - 5b - 4)$ and $(3b^2 - 5b - 7)$ . After fully simplifying the difference $(9b^2 - 5b - 4) - (3b^2 - 5b - 7)$ , the constant term in the resulting expression is ____.
An operations manager is comparing two production cost models represented by the polynomials $(9b^2 - 5b - 4)$ and $(3b^2 - 5b - 7)$ . To calculate the difference between these models, the manager evaluates $(9b^2 - 5b - 4) - (3b^2 - 5b - 7)$ . True or False: In the first step of this calculation, distributing the subtraction sign across the second polynomial results in the terms $-3b^2 + 5b + 7$ .

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