What type of algebraic expression is 4x + 5?
Last Updated :
30 Dec, 2023
The 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 defined as an algebraic expression.
What is an Algebraic Expression?
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.
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 ‘equals to’ sign.
Types of Algebraic Expression
Based on the number of terms in the expression, algebraic expressions are divided into 3 parts:
- Monomial Expression
- Binomial Expression
- Polynomial Expression
Monomial Expression
An expression that has only one term is termed a Monomial expression.
Examples of monomial expressions include 5x4, 3xy, 2x, 5y, etc.
Binomial Expression
An algebraic expression which is having two terms and unlike are termed as a binomial expression
Examples of binomial include 2xy + 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 include ax + by + ca, x3 + 5x + 3, etc.
32x + 15y is a polynomial of two terms in two variables x and y.
15ab + 55a + 25 is a polynomial of three terms in two variables a and b.
Other Types of Expression
We have other expressions also apart from monomial, binomial, and polynomial 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 14 + 5, 18 ÷ 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 4x + y, 5ab + 53, etc.
Some Important Algebraic Formulae
There are some terms of algebraic expression which basically used,
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2
(x + a)(x + b) = x2 + x(a + b) + ab
(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)
Example: If 2x2+3xy+4x+7 is an algebraic expression. Determine the equation.
Solution:
2x2, 3xy, 4x, and 7 are the Terms
Coefficient of term: 2 is the coefficient of x2
Constant term: 7
Variables: here x, y are variables
Factors of a term: If 2xy is a term, then its factors are 2, x, and y.
Like and Unlike terms : Example of like and unlike terms:
- Like terms: 4x and 3x
- Unlike terms: 2x and 4y
What type of algebraic expression is 4x + 5?
Answer:
An algebraic expression which is having two terms and unlike are termed as a binomial expression.
Here 4x + 5 has two monomials 4x and 5 and hence it is a binomial and every binomial is a type of polynomial.
Therefore, 4x + 5 is a binomial.
Similar Questions
Question 1: Examples of binomial Expression?
Answer:
A term and a number:
One term is an algebraic term and another term may be a number.
Example- 22a + 18, a – 28, 13/7 + ab2
Two Unlike Algebraic terms:
Two, unlike algebraic terms, may form a binomial.
Example- x + 2y, x + y2
Question 2: What type of algebraic expression is x3 + 5x + 3?
Answer:
An expression that has more than one term with non-negative integral exponents of a variable is termed a polynomial expression.
here, x3 + 5x + 3 has more than one term therefore it is polynomial expression.
Question 3: Simplify (x – 2)(3x + 5) and what type of expression it is?
Solution:
Given that: (x – 2)(3x + 5)
= x(3x + 5) – 2 (3x + 5)
= 3x2 + 5x – (6x + 10)
= 3x2 + 5x – 6x – 10
= 3x2 – x – 10
here 3x2 – x – 10 is a trinomial expression or polynomial expression
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