How are Algebraic Expressions Formed?

Basic concept of algebra taught us how to express an unknown value using letters such as x, y, z, etc.  These letters are termed here as variables. this expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is termed a coefficient.

An idea of expressing numbers using letters or alphabets without specifying their actual values is termed an algebraic expression.

In mathematics, an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, etc.. is called Algebraic Expression. These Expressions are made up of terms.  Algebraic expressions are equations when operations such as addition, subtraction, multiplication, division, etc. are operated upon any variable.

A combination of terms by the operations such as addition, subtraction, multiplication, division, etc. is termed an algebraic expression (or) a variable expression.

Examples: 2x + 4y – 7,  3x – 10, etc.

The above expressions are represented with the help of unknown variables, constants, and coefficients. The combination of these three terms is termed as an expression. Unlike the algebraic equation, It has no sides or an ‘equals to’ sign.

Some of its examples include

• 2x + 2y – 5
• 4x – 20
• 3x + 2

Various types of algebraic expressions are:

• Monomial Expression
• Binomial Expression
• Polynomial Expression

Monomial Expression

An expression that has only one term is termed a Monomial expression.

Examples of Monomial Expressions: 4x⁴, 2xy, 2x, 8y, etc.

Binomial Expression

An algebraic expression which is having two terms and unlike are termed as the binomial expression  

Examples of Binomial Expression: 4xy + 8, xyz + x², etc.

Polynomial Expression

An expression that has more than one term with non-negative integral exponents of a variable is termed a polynomial expression.

Examples of Polynomial Expression: ax + by + ca,  x³ + 5x + 3, etc.

Apart from monomial, binomial, and polynomial, there are some other types of expressions which are  

• Numeric Expression
• Variable Expression

Numeric Expression

An expression that consists of only numbers and operations, but never includes any variable is termed a numeric expression.

Some of the examples of numeric expressions are 11 + 5, 14 ÷ 2, etc.

Variable Expression

An expression that contains variables along with numbers and operations to define an expression is termed as A variable expression.

Some examples of a variable expression include 5x + y, 4ab + 33, etc.

Some important algebraic formulas are:

(a + b) = a² + 2ab + b²

(a – b) = a² – 2ab + b²

(a + b)(a – b) = a² – b²

(x + a)(x + b) = x² + x(a + b) + ab

An algebraic expression is formed from variables and constants using different operations.

It is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, etc.. these Expressions are made up of terms. Algebraic expressions are the equations when the operations such as addition, subtraction, multiplication, division, etc. are operated upon any variable.

A combination of terms by the operations such as addition, subtraction, multiplication, division, etc is termed as an algebraic expression (or) a variable expression.

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

Terms of Algebraic Equation: 2x², 3xy, 4x, and 7

Coefficient of Term: 2 is the coefficient of x², 3 is coefficient of xy, 4 is coefficient of x

Constant term: 7

Variables: Here x, y are variables

Like terms: 4x and 3x  

Unlike terms: 2x and 4y

Read More:

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

Question 1: Simplify 4 – 3(x – 1).

Solution:

Here we have

4 – 3(x – 1)

= 4 – 3x +3

= 7 – 3x = -3x + 7

Question 2: Find out the constant from the following algebraic expressions,

• x³ + 3x² – 4
• 2 + y⁵

Solution:

Constants are the terms that do not have any variable,

Therefore, in the first term -4 is the constant and in the second term 2 is the constant.

Question 3: Identify the various components of algebraic expressions: 6x + 3y – 4.  

Solution:  

Algebraic expression is constituted by the following parts:  

6x and 3y, where 6 and 3 are coefficients and x and y are variables. -4 is the constant part of the expression.

Question 4: Solve for x = 3 : x² – 4x + 5

Solution:

x² – 4x + 5

Here we have

3² – (4 × 3) + 5

= 9 – 12 + 5

= 14 – 12 = 2

What is an algebraic expression and example?

A mathematical expression including variables, constants, coefficients, and algebraic operations is called an Algebraic Expression. For example, 3x² + 7x – 11 is an algebraic expression.

Is 4 an algebraic expression?

No. 4 is not an algebraic expression, as an algebraic expression must have a variable and an operation.

What are the four types of algebraic expressions?

Four types of algebraic expressions are:

• Monomial Expression
• Binomial Expression
• Trinomial Expression
• Polynomial Expression

Who is the father of algebra?

Muhammad ibn Musa al-Khwarizmi is generally considered as father of Algebra.