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Chapter 3: Problem 2

Define the key terms. a. Coefficient b. Constant term c. Like terms d. Term e. Variable term

Short Answer

Expert verified
Coefficient: Multiplier of variables. Constant term: Value without variables. Like terms: Terms with same variables and powers. Term: Single mathematical expression. Variable term: Term containing a variable.

Step by step solution

01

Define Coefficient

A coefficient is a numerical or constant multiplier of the variables in an algebraic expression. For example, in the term 7x, 7 is the coefficient.
02

Define Constant Term

A constant term is a value in an algebraic expression that does not change and has no variables attached to it. For example, in the expression 5x + 3, the number 3 is the constant term.
03

Define Like Terms

Like terms are terms in an algebraic expression that have the same variables raised to the same powers, but they can have different coefficients. For example, 3x and 5x are like terms because both include the variable x.
04

Define Term

A term is a single mathematical expression that can be a number, a variable, or the product of numbers and variables. For example, in the expression 4y + 7, both 4y and 7 are terms.
05

Define Variable Term

A variable term is a term that contains a variable. For example, in the term 6z, 6 is the coefficient, and z is the variable term.

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Key Concepts

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

coefficient
In algebra, terms often include numbers and variables. The coefficient is the numerical part of a term. It multiplies the variable. For instance, in the expression 7x, the number 7 is the coefficient. It tells you how many times the variable x is being counted. Coefficients can be positive, negative, whole numbers, or fractions. They are essential for combining like terms in algebraic expressions.
constant term
A constant term is a term that does not have a variable. This means its value does not change. For example, in the algebraic expression 5x + 3, the number 3 is the constant term. Unlike terms with variables, constant terms stay the same no matter what values the variables might take. They are straightforward and help simplify algebraic operations.
like terms
Like terms are terms that have the same variable raised to the same power, although their coefficients can be different. For instance, in the expression 3x + 5x, both 3x and 5x are like terms because they both include the variable x. Identifying like terms helps in simplifying algebraic expressions, as they can be added or subtracted from one another.
term
A term in algebra is any single expression. It could be just a number, just a variable, or a combination of both. For example, in the expression 4y + 7, 4y and 7 are individual terms. Notice that terms are separated by the addition or subtraction operators in an expression. Recognizing individual terms is fundamental for solving and simplifying algebraic expressions.
variable term
A term that contains a variable is called a variable term. For example, in the term 6z, 6 is the coefficient, and z is the variable. Unlike constant terms, variable terms change their value depending on the value of the variable. Variable terms are crucial for creating and solving algebraic equations.

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Most popular questions from this chapter

Apply the appropriate property to simplify the expression. $$-3(25-m)$$

Solve the equation. $$p-6=-18$$

Demonstrate the commutative property of multiplication by evaluating the expressions for \(c=12\) and \(d=-4\). a. \(c \cdot d\) b. \(d \cdot c\)

Clear parentheses and combine like terms. $$7(a-4)+8$$

List the terms and identify each term as a variable term or a constant term. $$2 a+5 b^{2}+6$$
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