Types of Algebraic Expressions
Types of algebraic expressions may further be distinguished in the following five categories.
They are: monomial, polynomial, binomial, trinomial, multinomial.
1. Monomial: An algebraic expression which consists of one non-zero term only is called a monomial.
Examples of Monomials:
a is a monomial in one variable a.
10ab2 is a monomial in two variables a and b.5m2n is a monomial in two variables m and n.
-7pq is a monomial in two variables p and q.
5b3c is a monomial in two variables b and c.
2b is a monomial in one variable b.
2ax/3y is a monomial in three variables a, x and y.
k2 is a monomial in one variable k.
2. Polynomial: An algebraic expression which consists of one, two or more terms is called a polynomial.
Examples of polynomials:
2a + 5b is a polynomial of two terms in two variables a and b.
3xy + 5x + 1 is a polynomial of three terms in two variables x and y.
3y4 + 2y3 + 7y2 - 9y + 3/5 is a polynomial of five terms in one variable y.m + 5mn – 7m2n + nm2 + 9 is a polynomial of four terms in two variables m and n.
3 + 7x5 + 4x2 is a polynomial of three terms in one variable x.
3 + 5x2 - 4x2y + 5xy2 is a polynomial of three terms in two variables x and y.
x + 5yz – 7z + 11 is a polynomial of four terms in three variables x, y and z.
1 + 2p + 3p2 + 4p3 + 5p4 + 6p5 + 7p6 is a polynomial of seven terms in one variable p.
3. Binomial: An algebraic expression which consists of two non-zero terms is called a binomial.
Examples of binomials:
m + n is a binomial in two variables m and n.
a2 + 2b is a binomial in two variables a and b.5x3 – 9y2 is a binomial in two variables x and y.
-11p – q2 is a binomial in two variables p and q.
b3/2 + c/3 is a binomial in two variables b and c.
5m2n2 + 1/7 is a binomial in two variables m and n.
4. Trinomial: An
algebraic expression of three non-zero terms only is called a trinomial.
Examples of trinomial:
x + y + z is a trinomial in three variables x, y and z.
2a2 + 5a + 7 is a trinomial in one variables a.xy + x + 2y2 is a trinomial in two variables x and y.
-7m5 + n3 – 3m2n2 is a trinomial in two variables m and n.
5abc – 7ab + 9ac is a trinomial in three variables a, b and c.
x2/3 + ay – 6bz is a trinomial in five variables a, b, x, y and z.
5. Multinomial: An algebraic expression of two terms or more than three terms is called a multinomial.
Note: binomial and trinomial are the trinomials.
Examples of Multinomial:
p + q is a multinomial of two terms in two variables p and q.
a + b + c is a multinomial of three terms in three variables a, b and c.
a + b + c + d is a multinomial of four terms in four variables a, b, c and d.
x4 + 2x3 + 1/x + 1 is a multinomial of four terms in one variable xa + ab + b2 + bc + cd is a multinomial of five terms in four variables a, b, c and d.
5x8 + 3x7 + 2x6 + 5x5 - 2x4 - x3 + 7x2 - x is a multinomial of eight terms in one variable x.
These are the types of algebraic expressions explained with various types of examples.
● Terms of an Algebraic Expression
Types of Algebraic Expressions
Multiplication of Two Monomials
Multiplication of Polynomial by Monomial
Multiplication of two Binomials
Algebra Page
6th Grade Page
From Types of Algebraic Expressions to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Multiplication by Ten, Hundred and Thousand |Multiply by 10, 100 &1000
May 01, 25 11:57 PM
To multiply a number by 10, 100, or 1000 we need to count the number of zeroes in the multiplier and write the same number of zeroes to the right of the multiplicand. Rules for the multiplication by 1… -
Adding and Subtracting Large Decimals | Examples | Worksheet | Answers
May 01, 25 03:01 PM
Here we will learn adding and subtracting large decimals. We have already learnt how to add and subtract smaller decimals. Now we will consider some examples involving larger decimals. -
Converting Fractions to Decimals | Solved Examples | Free Worksheet
Apr 28, 25 01:43 AM
In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps: -
Expanded Form of a Number | Writing Numbers in Expanded Form | Values
Apr 27, 25 10:13 AM
We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its… -
Converting Decimals to Fractions | Solved Examples | Free Worksheet
Apr 26, 25 04:56 PM
In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…
● Terms of an Algebraic Expression - Worksheet
Worksheet on Types of Algebraic Expressions
Worksheet on Degree of a Polynomial
Worksheet on Addition of Polynomials
Worksheet on Subtraction of Polynomials
Worksheet on Addition and Subtraction of Polynomials
Worksheet on Adding and Subtracting Polynomials
Worksheet on Multiplying Monomials
Worksheet on Multiplying Monomial and Binomial
Worksheet on Multiplying Monomial and Polynomial
Worksheet on Multiplying Binomials
Worksheet on Dividing Monomials
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.