Multiplication of Two Monomials

Multiplication of two monomials means product of their numerical coefficients and product of their literal coefficients.



According to the power of literal quantities we can express, m2 = m × m and m3 = m × m × m. Here, m2 and m3 both are monomials.

Therefore, multiplication of m2 and m3 = m2 × m3

                                                    = (m × m) × (m × m × m)

                                                    = m × m × m × m × m

                                                    = m5

Or, in other way we can simply add the powers since the base is same. In case of m2 × m3 both have same base then we get, m2 + 3 = m5

Note: To multiply, the powers of like factors or same base are added.



Similarly, we can multiply the two monomials 7a2b and 5ab2 in two different ways.

7a2b and 5ab2

= 7a2b × 5ab2

= (7 × a × a × b) × (5 × a × b × b)

= (7 × 5) × (a × a × a) × (b × b × b)

= 35a3b3

or, in other way we can simply 7a2b × 5ab2

= (7 × 5) ∙ a2 + 1 ∙ b1 + 2

= 35a3b3

Therefore, to multiply two monomials, multiply their coefficients together and prefix their product to the product of letters in the monomials.


Examples on multiplication of two monomials:

1. Find the product of 9a2b3, 2b2c5 and 3ac2.

9a2b3 × 2b2c5 × 3ac2

= (9 × a × a × b × b × b) × (2 × b × b × c × c × c × c × c) × (3 × a × c × c)

= (9 × 2 × 3) × (a × a × a) × (b × b × b × b × b) × (c × c × c × c × c × c × c)

= 54 × a3 × b5 × c7

= 54a3b5c7



2. Find the product of -9x2yz3, 5/3xy3z2 and -7yz.

-9x2yz3 × 5/3xy3z2 × -7yz

= (-9 × 5/3 × -7) × (x2 × x) × (y × y3 × y) × (z3 × z2 × z)

Now we need to add the powers of the same bases i.e. x, y and z.

= (315/3) × (x2 + 1) × (y1 + 3 + 1) × (z3 + 2 + 1)

= 105 × x3 × y5 × z6

= 105x3y5z6

Terms of an Algebraic Expression

Types of Algebraic Expressions

Degree of a Polynomial

Addition of Polynomials

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials






Algebra Page

6th Grade Page

From Multiplication of Two Monomials 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.



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.

Share this page: What’s this?

Recent Articles

  1. Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

    May 18, 24 02:59 PM

    Rules for Comparison of Numbers
    Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…

    Read More

  2. Numbers | Notation | Numeration | Numeral | Estimation | Examples

    May 12, 24 06:28 PM

    Numbers are used for calculating and counting. These counting numbers 1, 2, 3, 4, 5, .......... are called natural numbers. In order to describe the number of elements in a collection with no objects

    Read More

  3. Face Value and Place Value|Difference Between Place Value & Face Value

    May 12, 24 06:23 PM

    Face Value and Place Value
    What is the difference between face value and place value of digits? Before we proceed to face value and place value let us recall the expanded form of a number. The face value of a digit is the digit…

    Read More

  4. Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns

    May 12, 24 06:09 PM

    Complete the Series Patterns
    We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r…

    Read More

  5. Worksheet on Bar Graphs | Bar Graphs or Column Graphs | Graphing Bar

    May 12, 24 04:59 PM

    Bar Graph Worksheet
    In math worksheet on bar graphs students can practice the questions on how to make and read bar graphs or column graphs. Test your knowledge by practicing this graphing worksheet where we will

    Read More

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