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Identifying Terms in an Expression
To identify the terms within an algebraic expression, locate the parts of the expression separated by addition () or subtraction () signs. Each separated part is a single term.
- In $9x^2 + 7x + 12, the addition signs divide the expression into three terms: $9x^2, $7x{12}$.
- In $8x + 3y, the addition sign separates two terms: $8x and $3y$.
A standalone constant such as qualifies as its own term, and terms with different variable parts—like $9x^2x squared) versus $7x (involving to the first power)—are counted as distinct terms.
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Ch.1 Foundations - Elementary Algebra @ OpenStax
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Coefficient of a Term
Like Terms in Algebra
Identifying Terms in an Expression
Monomial
A logistics coordinator uses the expression 25w + 15 to calculate the shipping cost of a package, where 25w represents the weight-based fee and 15 is a flat handling charge. What is the mathematical name for the individual components, 25w and 15, that are combined to form this expression?
In the business cost expression 4x + 500, the constant value 500 is considered an algebraic term even though it does not include a variable.
Identifying Components of a Service Cost Formula
In a warehouse management system, various mathematical components are used to track inventory and labor costs. Match each component from a warehouse manager's calculation formula to the description that correctly identifies its form as an algebraic term.
A freelance consultant calculates their total invoice using the expression $150 + 60h, where $150 is a flat travel fee and $60h is the labor charge. In mathematics, the individual building blocks of this expression, such as '$150' and '$60h$', are each known as a(n) ____.
Analyzing Production Cost Components
A small business owner uses the formula $9a + y + 7 to calculate monthly service expenses, where $9a is the cost of 9 units at price , is a variable utility charge, and $7$ is a fixed processing fee. Identify the three individual algebraic terms in this formula and arrange them in the order they appear from left to right.
Defining Algebraic Terms in Business Formulas
A retail manager uses the formula to calculate the total price of an order, where represents the price of items and is a flat shipping fee. In this context, and are individual algebraic terms. Based on the mathematical definition, what can an algebraic term consist of?
An office manager is setting up a spreadsheet to track service expenses using mathematical formulas. According to the definition of an 'algebraic term,' which of the following is NOT an example of a single algebraic term?
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A logistics coordinator uses the expression 45w + 12g + 150 to calculate the total shipping cost for a delivery, where 'w' represents the weight in pounds, 'g' represents the number of fragile items, and 150 is a flat handling fee. Which of the following correctly identifies the individual terms in this expression?
A medical billing specialist uses the expression 120v + 45m + 15 to calculate a patient's total charges. In algebra, the individual parts of this expression (120v, 45m, and 15) that are separated by the addition signs are each called a(n) ____.
A business administrator uses various algebraic expressions to track company costs and resource allocations. Match each financial expression with the correct number of terms it contains, based on the parts separated by addition () or subtraction () signs.
A project coordinator uses the expression $300p + 150h - 50 to estimate project costs. True or False: In this expression, the subtraction sign between $150h and $50 indicates that $150h and $50$ are two separate terms.
Identifying Billing Components in Service Invoices
Identifying Budget Components in Business Expressions
A logistics coordinator uses the expression $1200 + 45w + 30g - 15d$ to calculate the total shipping cost for a project. Arrange the following components in the correct order as they appear as individual terms in the expression, from left to right.
Analyzing Marketing Campaign Costs
A project coordinator uses the expression $2500 + 45h - 100d$ to estimate project costs. According to the rules for identifying terms in an algebraic expression, which specific symbols are used to define the boundaries between the individual terms?
A logistics manager uses the expression $15s^2 + 40s + 250s$) of a shipping container. According to the rules for identifying terms, which of the following is NOT an individual term in this expression?