Factorization when Monomial is Common

In factorization when monomial is common factor we know, that an algebraic expression is the sum or the difference of monomials.

In order to factorize follow the following steps:

Step 1: Write the algebraic expression.

Step 2: Find the HCF of all the terms of the given algebraic expression.

Step 3:  Express each terms of the algebraic expression as the product of H.C.F and the quotient when it is divided by the H.C.F.

i.e. divide each term of the given expression by the HCF.

Step 4:  Now use distributive property of multiplication over addition or subtraction to express the algebraic expression as the product of H.C.F and the quotient of the expression divided by the H.C.F.

i.e. write the given expression as the product of this HCF and the quotient obtained in step 2. 

Step 5:  Keep the H.C.F. outside the bracket and the quotients obtained within the bracket.


Solved examples of factorization when monomial is common:

1. Factorize each of the following: 

(i) 5x + 20

Solution: 

5x + 20

= 5(x + 4)


(ii) 2n2 + 3n

Solution:

2n2 + 3n

= n(2n + 3)


(iii) 3x2y - 6xy2

Solution:

3x2y - 6xy2

= 3xy(x - 2y)

(iv) 6ab - 9bc

Solution:


6ab - 9bc

= 3b(2a - 3c)


2. Factorize 6a2b2c + 27abc.

Solution:

The H.C.F. of 6a2b2c and 27abc = (H.C.F. of 6 and 27) × (H.C.F. of a2b2c and abc)

The H.C.F. of 6 and 27 = 3

The H.C.F. of a2b2c and abc = abc

Therefore, the H.C.F. of 6a2b2c and 27abc is 3abc.

Now, 6a2b2c + 27abc = \(3abc(\frac{6a^{2}b^{2}c}{3abc} - \frac{27abc}{3abc})\)

                              = 3abc(2ab + 9)

Therefore, the factor of 6a2b2c + 27abc are 3abc and (2ab + 9).



3. Factorize the expression:

18a3 - 27a2b

Solution:

18a3 - 27a2b

HCF of 18a3 and 27a2b is 9a2.

Therefore, 18a3 - 27a2b = 9a2(2a - 3b).





8th Grade Math Practice

From Factorization when Monomial is Common to HOME PAGE


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.



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.



Share this page: What’s this?

Recent Articles

  1. Multiplication of a Number by a 3-Digit Number |3-Digit Multiplication

    Mar 28, 24 06:33 PM

    Multiplying by 3-Digit Number
    In multiplication of a number by a 3-digit number are explained here step by step. Consider the following examples on multiplication of a number by a 3-digit number: 1. Find the product of 36 × 137

    Read More

  2. Multiply a Number by a 2-Digit Number | Multiplying 2-Digit by 2-Digit

    Mar 27, 24 05:21 PM

    Multiply 2-Digit Numbers by a 2-Digit Numbers
    How to multiply a number by a 2-digit number? We shall revise here to multiply 2-digit and 3-digit numbers by a 2-digit number (multiplier) as well as learn another procedure for the multiplication of…

    Read More

  3. Multiplication by 1-digit Number | Multiplying 1-Digit by 4-Digit

    Mar 26, 24 04:14 PM

    Multiplication by 1-digit Number
    How to Multiply by a 1-Digit Number We will learn how to multiply any number by a one-digit number. Multiply 2154 and 4. Solution: Step I: Arrange the numbers vertically. Step II: First multiply the d…

    Read More

  4. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Mar 25, 24 05:36 PM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More

  5. Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb

    Mar 25, 24 04:18 PM

    Multiplying 2-Digit Number by 1-Digit Number
    Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by

    Read More