Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

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What is an Algebraic Expression?

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. Also, solve questions in Algebraic Expressions Worksheets, at BYJU’S.

Examples

3x + 4y – 7, 4x – 10, etc.

These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign. Some of its examples include

3x + 2y – 5x – 202x2 − 3xy + 5

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Variables, Coefficient & Constant in Algebraic Expressions

In Algebra we work with Variable, Symbols or Letters whose value is unknown to us.

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In the above expression (i.e. 5x – 3),

x is a variable, whose value is unknown to us which can take any value.5 is known as the coefficient of x, as it is a constant value used with the variable term and is well defined.3 is the constant value term that has a definite value.

The whole expression is known to be the Binomial term, as it has two unlikely terms.

Types of Algebraic expression

There are 3 main types of algebraic expressions which include:

Monomial ExpressionBinomial ExpressionPolynomial Expression

Monomial Expression

An algebraic expression which is having only one term is known as a monomial.

Examples of monomial expressions include 3x4, 3xy, 3x, 8y, etc.

Binomial Expression

A binomial expression is an algebraic expression which is having two terms, which are unlike.

Examples of binomial include 5xy + 8, xyz + x3, etc.

Polynomial Expression

In general, an expression with more than one term with non-negative integral exponents of a variable is known as a polynomial.

Examples of polynomial expression include ax + by + ca,  x3 + 2x + 3, etc.

Other Types of Expression

Apart from monomial, binomial and polynomial types of expressions, an algebraic expression can also be classified into two additional types which are:

Numeric ExpressionVariable Expression

Numeric Expression

A numeric expression consists of numbers and operations, but never include any variable. Some of the examples of numeric expressions are 10 + 5, 15 ÷ 2, etc.

Variable Expression

A variable expression is an expression that contains variables along with numbers and operation to define an expression. A few examples of a variable expression include 4x + y, 5ab + 33, etc.

Algebraic Expression for Class 7

In Class 7, students will come across the terms of algebraic equations such as:

Coefficient of a termVariablesConstant Factors of a termTerms of equationsLike and Unlike terms

Examples of using these terms are given below.

If 2x2+3xy+4x+7 is an algebraic expression.

Then, 2x2, 3xy, 4x and 7 are the terms

Coefficient of term x2 = 2

Constant term = 7

Example of like and unlike terms: 

Like terms: 2x and 3x 

Unlike terms: 2x and 3y

Factors of a term:

If 3xy is a term, then its factors are 3, x and y.

Monomial, Binomial & Trinomial

Also, in grade 7 we will learn about types of expressions, such as monomial, binomial and trinomial. Let us see examples of each.

Monomial: 2x

Binomial: 2x+3y

Trinomial: 2x+3y+9

Addition and Subtraction of Algebraic Expressions

We can add and subtract like terms easily. 

Example: Add 3x + 5y – 6z and x – 4y + 2z.

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By adding both the expressions we get;

(3x + 5y – 6z) + (x – 4y + 2z)

Separating the like terms and adding them together:

(3x + x) + (5y – 4y) + (-6z + 2z)

4x + y – 4z

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Formulas

The general algebraic formulas we use to solve the expressions or equations are:

(a + b)2 = a2 + 2ab + b2(a – b)2 = a2 – 2ab + b2a2 – b2 = (a – b)(a + b)(a + b)3 = a3 + b3 + 3ab(a + b)(a – b)3 = a3 – b3 – 3ab(a – b) a3 – b3 = (a – b)(a2 + ab + b2)a3 + b3 = (a + b)(a2 – ab + b2)

Solved Problem on Algebraic Expression


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Example: Simplify the given expressions by combining the like terms and write the type of Algebraic expression.

(i) 3xy­­3 + 9x2 y3 + 5y3x

(ii) 7ab2 c2 + 2a3 b2 − 3abc – 5ab2 c2 – 2b2 a3 + 2ab

(iii) 50x3 – 20x + 8x + 21x3 – 3x + 15x – 41x3

Solution:

Creating a table to find the solution:


S.noTermSimplificationType of Expression
3xy­­3 + 9x2 y3 + 5y3x8xy3 + 9x2y3Binomial
27ab2 c2 + 2a3 b2 − 3abc – 5ab2 c2 – 2b2 a3 + 2ab2ab2 c2 − 3abc + 2abTrinomial
350x3 – 20x + 8x + 21x3 – 3x + 15x – 41x330x³Monomial