Is a variable considered a term?

Algebra is an upgraded discipline of mathematics that is the study of the manipulation of numerical values and symbols. These manipulations or operations are carried out to determine the unknown values represented by symbols or alphabets in the expression. Algebraic equations are associated with terms like a variable, constants, factors, and coefficient of variables.

Algebraic expressions

These are the mathematical expressions built up by the combination of a number of terms which consists of constants, variables (unknown values), and coefficient of variables along with mathematical operations like summation, subtraction, multiplication, and division.

Types of algebraic expression

On the basis of a number of terms present in an equation. Algebraic expressions are divided into three types.

• Monomial expression: The expressions which consist of a single term along with a mathematical operation attached to it are monomial expressions. For example, +1, 2xy, etc are the monomial expressions having a single term.
• Binomial expression: The expressions which consist of two terms bound with a mathematical operation are binomial expressions. For example, 2x + 1, 2x + 5y, etc are binomial expressions with two terms.
• Polynomial expression: The expression which consists of multiple numbers of terms along with mathematical operations attached to them is polynomial expression. For example, 2x + 3xy + 1, xy + yz + xz, etc are the polynomial expressions with multiple numbers of terms.

Term

A term is a mathematical phrase in which an algebraic expression is formed. A term either can be a variable, a constant with mathematical operation attached to it, or a product of variables or product of number and variable. An algebraic expression is composed of a single or a group of terms that are bonded with basic mathematical operations.

Here, the numbers or variables which are multiplied to form a term are called the factors. For example, if a term is 2xy then, its factors will be 5, x, and y.

Components of a Term

A term is composed of a combination of constants, variables, and coefficients of variables. These components are described below.

• Constants: Constants are fixed values that cannot be changed. The constants represent the known values in the expression. Every constant in an algebraic expression is attached with a basic operation.
• Variable: Variables are the unknown values in the expression represented by alphabetical letters like a,b,x,y, etc. The calculations are carried out to determine these unknown values of the equation.
• Coefficient: A coefficient is an integer or a fixed numerical value that is written along with a variable. The coefficients are multiplied by the variable. And if a variable is given without any integer its coefficient will be 1.

Is a variable considered a term?

Answer:

In mathematics, variables are the alphabetic representation of unknown values or quantities. These unknown values are determined with the help of various mathematical operations. 

These unknown quantities are not fixed values, unlike constants and coefficients. They are generally represented by alphabets like a, b, x or y, etc. The variables are divided into two types that are the dependent and independent variables.

“A variable separately if presentin an algebraic expression can be called as a term of that expression. If the variable is attached with some coefficient or an exponent is present on the variable, they all together will be called as a term.”

Types of variables

• Dependent variable: Dependent variables are the variables whose value is reliant on the other variable present in the same equation. The value of the dependent variable changes as per the estimation of the other variable is changed.

For example: let us consider an equation, y = 2x + 3. In this equation the value of variable ‘y’ is reliant on the value of ‘x’. The value of y will change as per the estimated value of x.

• Independent variable: Independent variables are the variables that are independent of other variables of the equation. Both the variables of these kinds of equations will be directly linked to each other.

For example: let us consider an equation, a = b^2, in this equation a is the dependent variable and b is the independent variable. Every value of b is independent of a.

Sample Problems

Question 1: What are bound variables?

Answer:

A bound variable is a variable that is bounded to a specific value or set of values called domains.

Question 2: What is a control variable?

Answer:

A variable that is kept the same during a scientific experiment is the control variable.

Question 3: What is a random variable?

Answer:

A random variable is a variable that can be derived in different values, each with an associated probability.

Question 4: What are the factors in the term xy.

Answer:

The factors of term xy are 1, x and y.

Question 5: What are the coefficients in the expression 2x + 5y?

Answer:

In the expression 2x + 5y, 2 and 5 are the coefficients of variable x and y respectively.

Question 6: What is the constant in the expression 3x + 4?

Answer:

In the expression 3x + 4, 4 is the constant.