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202 LearnersLast updated on October 22, 2025

Algebraic expressions contain constants and variables often connected by operations like addition, subtraction, multiplication, or division. Constants are fixed numerical values, while variables can vary.
To write mathematical statements more compactly, we use algebraic expressions. Each expression is made up of different parts terms, factors, and coefficients. A term is a section of an expression separated by mathematical operations like addition or subtraction.
Each term can include variables, constants, or a combination of both. The factors are the elements that are multiplied together within a term, and the variables are the symbols or letters that represent unknown quantities.
For example, 5x2 + 6x - 3
So far, we’ve learned that different parts of an expression are named term, factor, and coefficient. In this section, we will take a look at them in detail.
Terms
In an algebraic expression, terms are the individual parts separated by mathematical operations such as addition or subtraction. Each term can be a number, a variable, or a combination of both.
Depending on the number of terms, expressions are classified as monomials (one term), binomials (two terms), or trinomials (three terms).
For example, 5x2 + 2x + 3 here, the terms are 5x2, 2x, and 3, and they are connected by addition.
Factors
Factors are the multiplicative components of a term.
For example, in 3xy, the factors are 3, x, and y.
Coefficients
A coefficient is the number in front of a variable in a term. It shows how many times the variable is multiplied.
For example, in an expression like 3xy + 2x −5y + 7, the coefficients are:
3 for xy
2 for x
-5 for y
7 (constant term, no variable)
Understanding algebraic expressions can be tricky for many students, especially when it comes to identifying terms, factors, and coefficients. These tips and tricks will help you quickly recognize each part, avoid common mistakes, and solve problems with confidence.
Algebraic expressions are an essential part of mathematics, and students often confuse them with terms, factors, and coefficients. This is a common mistake that can be avoided. Here are some other common mistakes for you to avoid:
Terms, factors, and coefficients are used in algebraic expressions, which are in turn used in various fields to solve different types of problems. Here are some applications showing how terms, factors, and coefficients are used in real life.
Write the algebraic expression for the given statement: Lily has 3 apples fewer than twice the number Ben has.
2b - 3
Let b be the number of apples Ben has
So to find twice the number of apples, multiply 2 by b.
Lily has 3 apples fewer than twice the number of Ben’s apples, i.e., 2b - 3 if written as an expression.
Therefore, the number of apples Lily has is 2b - 3.
Identify the terms, factors, and coefficients in 4x² - 7x + 10
Terms: 4x2 -7x, 10
The term is the part of an expression that is separated by + or -. Each of the terms can be broken down into factors, and the coefficients are the numbers that are multiplied by the variable.
Identify the term, factor, and coefficient in 6a² b
Terms: 6a2b
Factors: For 6a2b: 6, a, a, and b
Coefficient of a2b: 6
Variable part: a2b
The term 6a²b consists of factors: the coefficient 6 and the variable part a²b. Remember, a² means a × a, so the factors include two a’s and one b.
Write an algebraic expression to represent her total cost: Sarah rents a bike for a flat fee of $20 and pays $3 for each additional hour she uses it.
20 + 3h
Let h be the number of extra hours
Flat fee is $20
The extra charge is $3 per hour, so it is represented as 3h.
So, the total cost is 20 + 3h
Identify the term, factor, and coefficient in x³ + 5x² + 5x + 1
Terms are the parts of an expression separated by + or –. Each term can be broken into factors, and the coefficient is the number multiplied by the variable part. The constant is the term with no variable.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.






