Identifying Terms In an Algebraic Expression - GeeksforGeeks (2024)

Number of terms in an algebraic expression depends on how the expression is written and structured. In algebra, a term is a single mathematical expression that might be a number, a variable, or the product or quotient of numbers and variables. Terms are typically separated by “+” or “-” signs.

An algebraic expression is an expression composed of various components, such as variables, constants, coefficients, and arithmetic operations. These components form various parts of the algebraic expressions.

What is Algeabric Expression?

An algebraic expression is a linear equation composed of any number of variables. The highest power of the variable is known as the degree.

An algebraic expression containing one variable is monomial, two variables are binomial, and so on. For example, if we assume an expression to be,

2x+5

Here, the parts of the expression are as follows:

• Terms are 2x and 5
• Coefficient of the expression is 2
• Constant is 5
• Variable is x
• Mathematical operators used are plus (+) and minus (-).

What are Terms?

Terms of an algebraic expression are known as the components of the expression. An algebraic expression may be composed of one or more terms. A term of an expression may be a constant, a variable, a product of more than two variables (xy), or a product of a variable and a constant.

Coefficient Definition

A coefficient is an integer that is the constant which accompanies the variable. To summarise, a coefficient in an algebraic expression is considered the numerical factor of a term that is composed of constants and variables. Coefficients of the terms may be positive or negative.

They may be fractional in nature. For instance, in the term 2x, 2 is the coefficient for the variable x. The terms with no constant, that is with no numerical factor along with them have a unit coefficient. For instance, in the term z, +1 is the coefficient for the variable z. Similarly, we have, -5/2 as the coefficient of the term –5/2xy².

Constant Definition

Constant is the term in the algebraic expression which is constituted of only integers. These terms contain variable counterparts. These values are fixed in nature since there is no variable accompanying them.

Therefore, these terms have a fixed value throughout, since no change can occur in these. Terms may only be defined by constants. For instance, in the expression 7x² + 3xy + 8, the constant term in this expression is 8.

Variable Definition

Variables are terms composed of undefined values, which may assume different integer values on substituting them with different integers.

A variable term can be composed of one or more variables, where the variables may or may not be the same. For example, we have, x³ which is a term composed of x raised to the power of 3, and xyz is composed of three different variables.

For instance, x³ can be 8 where the value of x = 2.

Some of the examples of terms are:

• 12x: Constant term = 12; Variable term = x

• 42a: Constant = 42; Variable = a

• xy: Variables = x and y

• 89: Constant = 89

• mn: Constant = 1; Variables = m and n

Read More:

• Multiplication of Algebraic Expression
• Division of Algebraic Expressions
• Like and Unlike Algebraic Terms

Sample Questions on Terms in Algebraic Expression

Q1. Identify the terms, like terms, coefficients, and constants in the expression.

12m – 24n + 10 + m – 17

Solution:

Here, we have,

12m – 24n + 10 + m – 17

First, rewrite the subtractions as additions.

12m – 24n + 10 + m – 17 = 12m + (-24n) + 10 + m + (-17)

Therefore,

Terms: 12m, (-24n), m, 10, and (-17).

Like terms are the ones that contain the same variable

12m and m are a pair of like terms.

Constant terms 10 and -17 are like terms.

Coefficients: 12 is coefficient of m,

-24 is the coefficient of n

1 is the coefficient of m.

Therefore, the coefficients are 12, (-24), and 1.

Constants: 10, -17

Q2. Compute the value of x in the equation 2x + 20 = 40

Solution:

Given,

2x + 20 = 40

⇒ 2x + 20 = 40

⇒ 2x = 40 – 20

⇒ 2x = 20

⇒ x =20/2 = 10

Value of x in the equation 2x + 20 = 40 is 10.

Q3. Find the Variable, coefficient, constant, and terms of the algebraic expression

90x + 22y – 31

Solution:

Here given algebraic expression

90x + 22y – 31

We have to find Variable, coefficient, constant, and terms

Variables: x and y

Terms: 90x, 22y and 31

Constant: 31

Coefficient: 90 of x and 22 of y.

FAQs on Terms in Algebraic Expression

What are 5 term algebraic expressions?

Algebraic expression with 5 terms is called a polynomial.

How to find terms of an algebraic expression?

Terms in an algebraic expression are separated using + and – operator and so to find number of terms in an algebraic expression we check for + and – operator in algebraic expression.

What are terms in algebraic formula?

Components added or subtracted in an algebraic formula are called terms.