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Chapter 2: Problem 91

In the following exercises, list the terms in the given expression. $$10 y^{3}+y+2$$

Short Answer

Expert verified
The terms in the expression are: \(10y^{3}, y, 2\).

Step by step solution

01

- Identify the Terms

In a mathematical expression, terms are separated by addition (+) or subtraction (-) operators. Identify each part of the expression that is separated by these operators.
02

- List the Terms

Write down each term of the expression separately. For the given expression \(10y^{3} + y + 2\), the terms are: \[10y^{3}, \ y, \ 2\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Terms in Algebra
In algebra, an expression consists of a combination of numbers, variables, and operators such as addition (+) and subtraction (-).
Let's take a deeper look into the concept of terms:
Terms are individual parts of an expression that are separated by addition or subtraction operators.
Each term can be a number, a variable, or a product of numbers and variables.
  • Example: In the expression \(5x^2 - 3x + 2\), the terms are \(5x^2\), \(-3x\), and \(2\).
  • A term without a variable is called a constant; for instance, \(2\) in the above example.
  • A term with a variable is either a polynomial term (e.g., \(5x^2\)) or a linear term (e.g., \(-3x\)).
Recognizing terms is fundamental as it helps in performing operations like addition, subtraction, and factoring in algebra.
Mathematical Expressions
A mathematical expression is a combination of numbers, variables, and operators (like +, -, *, and /) grouped together to represent a value.
Expressions can be simple or complex:
  • Simple expressions: \(4x + 7\)
  • Complex expressions: \(3x^2 - 4xy + 5y - 6\)
Key points about expressions:
  • They do not include equality signs; thus, they are not equations or inequalities.
  • Every expression can be broken down into its terms.
  • Each part of an expression that is separated by addition or subtraction is called a term.
The given example \(10y^{3} + y + 2\) is an algebraic expression composed of three terms.
Addition and Subtraction Operators
Addition and subtraction operators play a crucial role in forming expressions. They separate terms within the expression and indicate how they should be combined or compared.
  • Addition Operator (+): Combines two or more terms. For instance, in \(4x + 3\), the plus sign combines \(4x\) and \(3\).
  • Subtraction Operator (-): Deducts one term from another. In \(5x - 2\), the minus sign deducts \(2\) from \(5x\).
These operators help to clearly identify each term in an expression. In the example \(10y^{3} + y + 2\), the addition operators separate the three distinct terms: \(10y^{3}\), \(y\), and \(2\). Recognizing these operators and the terms they separate is fundamental in algebra for simplifying, solving, or evaluating expressions.

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