Algebraic expressions and identities are the idea of representing some unknown quantities whose real values are not known to us. We do so with the help of english letters. An algebraic expression can be a combination of both variables and constants. Algebraic expressions are a foundation for higher studies in algebra which is dealt as a separate branch of mathematics. They help us solve and describe mathematical relationships and solve equations and are widely used in trigonometry, economics, machine learning, etc.
JEE Main 2025: Sample Papers | Mock Tests | PYQs | Study Plan 100 Days
JEE Main 2025: Maths Formulas | Study Materials
JEE Main 2025: Syllabus | Preparation Guide | High Scoring Topics
This article is about the concept of Class 8 maths algebraic expressions and identities. We will learn about what are algebraic expressions class 6, algebraic expression class 7, algebraic expression class 8, multiplication and division of such expressions, types of algebraic expressions, how to identify variables and constants in an expression and class 8 algebraic expressions questions and answers and much more in this article.
Algebraic expression is an expression that is made up of combining variables and constants, along with basic algebraic elementary operations like addition, subtraction, multiplication or division. It is the terms that finally make up an algebraic expression. So we can say that an expression is made up of various parts combined together.
For Example
We must note that unlike the algebraic equation, an algebraic expression has no sides or is equal to a sign. Some examples listed below:
-
-
In the above expression (i.e.
- x is a variable, whose value is unknown to us and takes any random value.
- 20 is known as the coefficient of
- 70 is the constant value term that has a definite value.
There are 3 main types of algebraic expressions which include:
Monomial Expression: An algebraic expression that has only one term.
For example,
Binomial Expression: An algebraic expression that has two terms, which are unlike.
For example,
Polynomial Expression: An algebraic expression with more than one term with non-negative integral exponents of a variable.
For example
An algebraic expression can also be categorised into two additional types as:
Numeric Expression: It consists of numbers and operations, but do not include any variable. Few examples are
Variable Expression: It contains variables along with numbers and operation to define an expression. For example
We will come across the terms of algebraic expressions such as:
If
Then,
Coefficient of term
Coefficient of term
Coefficient of term
Constant term
Now we define certain kinds of terms with their examples:
Like terms can be defined as those that have same variable. For example,
Unlike terms can be defined as those that have different variable. For example,
Factors of a term If 3 pq is a term, then its factors are
The operations on algebraic expressions include operations like addition, subtraction, multiplication and division of algebraic expressions.
Any two or more algebraic expressions can be added and subtracted. We can add and subtract like terms of an algebraic expressions easily.
Example: Add
By adding both the expressions we get;
Separating the like terms and adding them together:
In this process, we multiply every term of the first expression with every term of the second expression and at last combine all the products. So, we go to one particular term in an expression and then perform the desired arithmetic operation with every other term of another expression. For example,
-
Another example:
-
We factor out the numerator and the denominator, cancel the possible terms, and simplify the rest. For example,
-
Another example:
-
Now, let us look into some algebraic expressions and identities.
The general algebraic formulas used to solve the expressions or equations are:
-
-
-
-
-
-
-
Now let us look into some algebraic expressions examples.
Example 1: There are 20 apples in a bag. Write the algebraic expression for the number of apples in
Solution: The number of apples in one bag
Example 2: What type of algebraic expression is
Solution:
Example 3: Is 22a/x a monomial expression? Justify your answer.
Solution: The expression has a single non-zero term, but the denominator of the expression is a variable. So it is not a monomial.
Example 4: Add the following algebraic expressions:
Solution: The given algebraic expressions have no like terms. Hence their sum is
Example 5: Simplify the given algebraic expressions by combining the like terms and write the type of Algebraic expression.
(i)
(ii)
Solution: Creating a table to find the solution:
S.no | Term | Simplification | Type of Expression |
---|---|---|---|
1 | Binomial | ||
2 | Trinomial |
An algebraic expression is nothing but a variable expression described using its terms, operations on the terms. For example, z + 38 can be described as "38 more than xz".
A term can be a variable alone, a constant alone or it can be a combination of both attached with any operator.
They help us solve real life problems ,perform mathematical calculations.For example, instead of saying cost of 2 oranges and 3 cherries we can say
Yes, 71 is an algebraic expression, since it is a monomial.
An algebraic expression is defined as any number, variable, or different operations combined together, whereas an equation is two different algebraic expressions combined together with equal to sign.
20 Jan'25 04:04 PM
20 Jan'25 03:52 PM
20 Jan'25 03:28 PM
20 Jan'25 02:14 PM
20 Jan'25 02:00 PM
12 Feb'24 04:54 PM
29 Jan'24 05:47 PM
29 Jan'24 05:26 PM
28 Jan'24 09:42 PM