1Cademy - Simplifying $$a^2 + 7b^2

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Adding and Subtracting Polynomials

Example

Simplifying $a^2 + 7b^2 - 6a^2$

To simplify the polynomial expression $a^2 + 7b^2 - 6a^2$ , start by identifying the like terms. The terms $a^2$ and $-6a^2$ both share the identical variable part $a^2$ , making them like terms. The term $7b^2$ has a different variable part and is therefore not a like term. Rearrange the expression to group the like terms together:

$a^2 - 6a^2 + 7b^2$

Combine the like terms by adding their coefficients. The implicit coefficient of $a^2$ is $1$ , so $1 - 6 = -5$ , which gives $-5a^2$ . The term $7b^2$ has no like term, so it remains unchanged. The simplified polynomial is:

$-5a^2 + 7b^2$

Updated 2026-06-03

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OpenStax Intermediate Algebra

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You are reviewing the quarterly budget formulas for your department. The formula used to calculate a specific overhead cost is given by the expression $a^2 + 7b^2 - 6a^2$ , where $a$ represents administrative parameters and $b$ represents building maintenance parameters. To clean up the spreadsheet, you need to combine the like terms. Which of the following represents the correctly simplified expression?
A facility manager is auditing floor space allocations for two types of storage units, modeled by variables $a$ and $b$ . The total area is initially recorded by the formula $a^2 + 7b^2 - 6a^2$ . Arrange the following steps in the correct order to simplify this expression for the final audit report.
An industrial engineer is streamlining a production efficiency formula represented by the expression $a^2 + 7b^2 - 6a^2$ . To ensure the data model is accurate, match each component of the expression or the simplification process with its correct description.
A logistics coordinator is simplifying the shipping cost formula $a^2 + 7b^2 - 6a^2$ for a quarterly report. To correctly combine the $a^2$ and $-6a^2$ terms, the coordinator must recall the value of the implicit coefficient of the first term. The numerical value of the coefficient for $a^2$ is ____.
Identifying Like Terms in Financial Formulas
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Auditing a Departmental Cost Model

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