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Adding
Find the sum of two trinomials:
Step 1 — Identify like terms: The -terms are and ; the -terms are and ; the constants are and .
Step 2 — Rearrange to group like terms together: Using the Commutative Property of Addition, reorder so that matching terms are adjacent:
Step 3 — Combine like terms: Add the coefficients within each group: gives ; gives ; .
The sum is .
This example demonstrates that adding two polynomials requires no special rules beyond identifying and combining like terms — the same three-step process used for simpler expressions applies directly when entire polynomials are added together.
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Elementary Algebra @ OpenStax
Ch.6 Polynomials - Elementary Algebra @ OpenStax
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Combining Like Terms in
A warehouse supervisor is training a new employee on how to simplify inventory records using algebra. Match each step of the 'Combining Like Terms' process with its correct description based on the standard procedure.
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A project coordinator is simplifying a budget report where different expense categories are represented by algebraic variables. Arrange the standard steps of the 'Combining Like Terms' procedure in the correct sequence to help them simplify the expression.
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Combining Like Terms in
Learn After
An inventory manager is combining two stock reports represented by the polynomials (5y^2 - 3y + 15) and (3y^2 - 4y - 11). According to the standard procedure for adding polynomials, which mathematical property is used to rearrange the terms so that like terms are adjacent?
A warehouse manager is merging two inventory reports where stock levels are modeled by the polynomials (5y^2 - 3y + 15) and (3y^2 - 4y - 11). Match each set of like terms from the reports to their combined result in the total stock model.
An operations manager is combining two production models represented by the polynomials and . After adding the two models and combining like terms, the coefficient of the term in the resulting simplified polynomial is ____.
A logistics coordinator is merging two resource allocation models represented by the polynomials and . To calculate the total combined resource requirement, the coordinator must follow a standard three-step process. Arrange the following actions in the correct order as they would be performed in this procedure.
A business analyst is calculating the total estimated cost for a project by adding two expense models: and . True or False: When combining the matching terms and , the analyst should add the exponents to get a result of .
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A budget analyst is merging two cost-projection models represented by the polynomials and . According to the first step of the standard procedure for adding these models, which pair of values represents the constant terms?
A revenue analyst is merging two financial models represented by the polynomials and . In the first step of adding these models, the analyst identifies and as 'like terms'. What is the primary reason these two terms are classified as like terms?